#Random Variable And Distribution Function Assignment Homework Help
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Random Variable And Distribution Function Assignment Homework Help
https://www.statisticshomeworktutors.com/Random-Variable-And-Distribution-Function.php
Statisticshomeworktutors assures to provide you with well-structured and well-formatted solutions and our deliveries have always been on time whether it’s a day’s deadline or long. You can anytime buy assignments online through us and we assure to build your career with success and prosperity. So, if you have an assignment, please mail it to us at [email protected]. They solve it from the scratch to the core and precisely to your requirement. The basic topics that are normally considered part of college Random Variable and Distribution Function that we can help with:
pmf of Y = g(X) Â
Probability Density Function (pdf) and connection with pmf     Â
Probability density functions  Â
Probability distribution
Probability distribution and densities (cdf, pmf, pdf) Â Â Â Â Â
Random element
Random function     Â
Random measure     Â
Random number generator produces a random value    Â
Randomness   Â
Relation with pdf and pmf    Â
Stochastic process    Â
Term life insurance and death probability  Â
Testing the fit of a distribution to data
The conditional distribution function and conditional probability density function    Â
Uniform and exponential random variables Â
Visualizing a binomial distribution Â
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 Task QUESTION 1 Decision Analysis Guide to marks: 20 marks- 6 for a, 2 each for b1 & b2, 3 each for b3 & b4, 4 for b5 Show all calculations to support your answers. You may follow the methods shown in the mp4 on Decision Analysis for a way to do part (b) of this question if you wish. (a) Discuss the differences among decision making under certainty, under risk and under complete uncertainty. (b) Bikram Shrestha is considering investing some money that he inherited. The following payoff matrix gives the profits that would be realised during the next year for each of the investments that Bikram is considering. Good Economy Poor Economy Share market $80,000 ($20,000) Bonds 30,000 20,000 Real estate 25,000 15,000
Answer the following questions. Each answer must be supported with appropriate calculations and/or a table of figures, and you must state for questions 1 to 4 which alternative would be selected. 1 Which alternative would an optimist choose? 2 Which alternative would a pessimist choose? 3 Which alternative is indicated by the criterion of regret? 4 Assuming probability of a good economy = 0.3 using expected monetary values what is the optimum action? 5 What is the expected value of perfect information? QUESTION 2 Value of information Guide to marks: 20 marks – 4 for a, 8 for b, 2 for c, 6 for d Show all calculations to support your answers. You may follow the methods shown in the mp4 on Value of info for a way to answer this question if you wish, but however you do the calculations you must specifically provide answers to the 4 questions. DO NOT ROUND probability calculations with Round Function. You may display them to 2 decimal places if you like but do not round in memory. Jerry is thinking about opening a bicycle shop. He can open a large shop (a1) or a small shop (a2). He believes that a large shop would earn a profit of $80,000 if the market is good (s1) but would lose $40,000 if the market is poor (s2). A small shop would return $30,000 profit in a good market and a loss of $10,000 in a poor market. Jerry believes that there is a 50-50 chance that the market will be good. (a) What should Jerry do? Show calculations. A friend would charge him $3,000 for some market research providing.one of two signals, that the market is favourable or unfavourable. His past record is such that 80% of the time he would correctly provide a favourable market prediction when the market is good and 60% of the time he would correctly provide an unfavourable market prediction when the market is poor. (b) Revise the prior probabilities in light of his friend’s track record. (c) What is the posterior probability of a good market given that his friend has provided an unfavourable market prediction? (d) What is the expected net gain or loss from engaging his friend to conduct the market research? Should his friend be engaged? Why?
QUESTION 3 Monte Carlo Simulation This is a work integrated assessment item. The tasks are similar to what would be carried out in the workplace. Guide to marks: 20 marks – 12 for a, 2 for b, 6 for c Tully Tyres sells cheap imported tyres. The manager believes its profits are in decline. You have just been hired as an analyst by the manager of Tully Tyres to investigate the expected profit over the next 12 months based on current data. • Monthly demand varies from 100 to 200 tyres – probabilities shown in the partial section of the spreadsheet below. • The average selling price per tyre follows a discrete uniform distribution ranging from $60 to $80 each. This means that it can take on equally likely integer values between $60 and $80 – more on this below. • The average profit margin per tyre after covering variable costs follows a continuous uniform distribution between 20% and 30% of the selling price. • Fixed costs per month are $1500. (a) Using Excel set up a model to simulate the next 12 months to determine the expected average monthly profit for the year. You need to have loaded the Analysis Toolpak Add-In to your version of Excel. You must keep the data separate from the model. The model should show only formulas, no numbers whatsoever. You can use this template to guide you:
Tully Tyres DATA Prob Cum prob Demand Selling Price $60 $80 0.05 100 Monthly Fixed cost $1,500 0.10 120 Profit Margin 20% 30% 0.20 140 0.30 160 0.25 180 0.10 200 1.00 MODEL Selling Profit Fixed Month RN 1 Demand Price RN 2 Margin Costs Profit
• The first random number (RN 1) is to simulate monthly demands for tyres. • The average selling price follows a discrete uniform distribution and can be determined by the function =RANDBETWEEN(60,80) in this case. But of course you will not enter (60,80) but the data cell references where they are recorded. • The second random number (RN 2) is used to help simulate the profit margin. • The average profit margin follows a continuous uniform distribution ranging between 20% and 30% and can be determined by the formula =0.2+(0.3-0.2)*the second random number (RN 2). Again you do not enter 0.2 and 0.3 but the data cell references where they are located. Note that if the random number is high, say 1, then 0.3-0.2 becomes 1 and when added to 0.2 it becomes 0.3. If the random number is low, say 0, then 0.3-0.2 becomes zero and the profit margin becomes 0.2. • Add the 12 monthly profit figures and then find the average monthly profit. Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show the grid (ie., row and column numbers) and be copied from Excel and pasted into Word. See Spreadsheet Advice in Interact Resources for guidance. (b) Provide the average monthly profit to Tully Tyres over the 12-month period.. (c) You present your findings to the manager of Tully Tyres. He thinks that with market forces he can increase the average selling price by $20 (ie range from $80 to $100) without losing sales. However he does suggest that the profit margin would then increase to range from 22% to 32%. He has suggested that you examine the effect of these changes and report the results to him. Change the data accordingly in your model to make the changes and paste the output in your Word answer Then write a report to the manager explaining your conclusions with respect to his suggestions. Also mention any reservations you might have about the change in selling prices. The report must be dated, addressed to the Manager and signed off by you. (Word limit: No more than 150 words)
QUESTION 4 Regression Analysis Guide to marks: 20 marks – 5 for a, 10 for b, 3 for c, 2 for d Belinda, the accountant at Murray Manufacturing Company wants to identify cost drivers for support overhead costs. She has the impression that the staff spend a large part of their time ensuring that the equipment is correctly set up and checking the first units of production in each batch. Deborah has collected the following data for the past 12 months: Month OH Cost MH Batches 1 $80,000 2,200 300 2 40,000 2,400 120 3 63,000 2,100 250 4 45,000 2,700 160 5 44,000 2,300 200 6 48,000 3,800 170 7 65,000 3,600 260 8 46,000 1,800 160 9 33,000 3,200 150 10 66,000 2,800 210 Total 530,000 26,900 1,980
(a) Using the high-low method to estimate support overhead costs based on machine hours, what would be the estimated support overhead costs (to the nearest $) for a month in which 3,000 machine hours were used? (b) Using Excel, perform three regression analyses to regress Overhead Cost against Machine Hours, then against Batches, then against both of them simultaneously. Paste your results into Word. State the cost equation from each. Analyse and comment on the results of each regression as you perform it and determine the best one to use as a basis for future use. (c) If you had to settle for the results of a simple regression, which one would you use and why? (d) Using the best regression result determine the projected Overhead Cost in a month in which there were 2000 machine hours worked and 150 batches produced. QUESTION 5 CVP Analysis Guide to marks: 20 marks – 4 for a, 4 for b, 4 for c, 8 for d Show all calculations to support your answers. A manufacturer can make two products, A and B. The following data are available:B Product A B Total Sales price per unit $10 $20 Variable cost per unit $5 $12 Total fixed costs $4,000
(a) Calculate the unit contribution margin for each product. (b) This month the manufacturer will specialise in making only Product B. How many does he need to sell to break even? (c) If they specialise in making only A what is the breakeven sales volume for the month in sales dollars? (d) He now decides to manufacture both A and B this month in the ratio of 2 A to 1 of B. (i) How many of each product must be sold to earn a profit of $5,000 before tax for the month? (ii) How many of each product must be sold to earn a profit of $21,000 after tax (of 30c in the dollar) for the month? END OF ASSIGNMENT 3
Rationale This assessment task covers topics 3,4,5,6 and 8: Decision analysis and value of information, simulation, correlation and regression analysis and CVP analysis. Specifically, it seeks to assess your ability to complete the following subject learning outcomes: • apply decision theory to business situations • use simulation in complex decisions • demonstrate understanding of the application of statistical hypothesis testing in regression analysis • apply CVP analysis to product mix decisions involving single and multiple products Marking criteria Assessment Item 3 The criteria described below will not apply to all parts of all questions but describe the standards expected where the question requirements are appropriate. It is expected that all students will complete their own work with no collusion with other students.
Criteria High Distinction Distinction Credit Pass Apply decision analysis to business situations Completely correct application of rational decision making techniques to business problems including ability to evaluate further information prior to decisions Mostly correct application of rational decision making techniques to business problems including the correct evaluation of further information prior to decisions Some difficulty in correctly applying rational decision making techniques to business problems including somewhat correct evaluation of further information prior to decisions Weakness in applying rational decision making techniques to business problems and difficulty in evaluating further information prior to decisions Use simulation in complex decisions Completely correct use of Excel to simulate decision situations involving probabilistic states of nature Mostly correct use of Excel to simulate decision situations involving probabilistic states of nature Few errors in use of Excel to simulate decision situations involving probabilistic states of nature Some weakness in use of Excel to simulate decision situations involving probabilistic states of nature Hypothesis testing in regression analysis Completely correct application of t-tests to determine significance of independent variables Mostly correct application of t-tests to determine significance of independent variables Some difficulty in correctly applying t-tests to determine significance of independent variables Weakness exhibited in understanding the application of t-tests to determine significance of independent variables Apply CVP analysis to product mix decisions Correct use of CVP analysis to single and multi-product firms Mostly correct use of CVP analysis to single and multi-product firms Correct use of CVP analysis to single product firms but some difficulty with multi-product firms Mostly correct use of CVP analysis to single product firms but less confident with multi-product firms
Presentation You should refer to the marking criteria for each the assessment item. You should also folow the directions given in each question.. Requirements: 1. Present answers in the same sequence as the questions set. 2. The front page of your assessment should consist of: • subject code and subject name • your name and student number • assessment item number. 3. Other pages should include: • statement of academic integrity • list of questions attempted • student name and number on each page submitted • pages should be numbered • bibliography on last page. The following link provides study resources such as referencing, writing, grammar, punctuation and study planning:
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HLT 362V Complete Course New Version
HLT 362V Complete Course New Version
HLT362V
HLT 362V Module 1 Mean Variance Standard Deviation
Please type you answer in the cell beside the question.
1. Identify the sampling technique being used. Every 20th patient that comes into the emergency room is given a satisfaction survey upon their discharge.
a. random sampling
b. cluster sampling
c. systematic sampling
d. stratified sampling
e. none of the above
2. The formula for finding the sample mean is ______________.
3. The formula for finding sample standard deviation is ________________.
HLT 362V Module 1 Exercise 16 Done
1- The researchers analyzed the data they collected as though it were at what level of measurement? (Your choices are: Nominal, Ordinal, Interval/ratio, or Experimental)
2- What was the mean posttest empowerment score for the control group?
3- Compare the mean baseline and posttest depression scores of the experimental group. Was this an expected finding? Provide a rationale for your answer.
4- Compare the mean baseline and posttest depression scores of the control group. Do these scores strengthen or weaken the validity of the research results? Provide a rationale for your answer.
5- Which group’s test scores had the least amount of variability or dispersion? Provide a rationale for your answer.
6 – Did the empowerment variable or self-care self-efficacy variable demonstrate the greatest amount of dispersion? Provide a rationale for your answer.
7 – The mean (X ̅) is a measure of a distribution while the SD is a measure of its scores. Both X ̅ and SD are statistics.
8 – What was the mean severity for renal disease for the research subjects? What was the dispersion or variability of the renal disease severity scores? Did the severity scores vary significantly between the control and the experimental groups? Is this important? Provide a rationale for your answer.
9 – Which variable was least affected by the empowerment program? Provide a rationale for your answer.
10 – Was it important for the researchers to include the total means and SDs for the study variables in Table 2 to promote the readers’ understanding of the study results? Provide a rationale for your answer.
HLT 362V M2 Population Sampling Distribution
For a normal distribution that has a mean of 100 and a standard deviation of 8. Determine the Z-score for each of the following X values:
X = 108
X = 112
X = 98
X = 70
X = 124
Use the information in 1 A to determine the area or probability of the following:
P(x > 108)
P(x
HLT 362V Week 2 Module 2 Exercise 29
1. Assuming that the distribution is normal for weight relative to the ideal and 99% of the male participants scored between (-53.68, 64.64), where did 95% of the values for weight relative to the ideal lie? Round your answer to two decimal places.
2. Which of the following values from Table 1 tells us about variability of the scores in a distribution?
3. Assuming that the distribution for General Health Perceptions is normal, 95% of the females’ scores around the mean were between what values? Round your answer to two decimal places.
4. Assuming that the distribution of scores for Pain is normal, 95% of the men’s scores around the mean were between what two values? Round your answer to two decimal places.
5. Were the body image scores significantly different for women versus men? Provide a rationale for your answer.
6. Assuming that the distribution of Mental Health scores for men is normal, where are 99% of the men’s mental health scores around the mean in this distribution? Round your answer to two decimal places.
7. Assuming that the distribution of scores for Physical Functioning in women is normal, where are 99% of the women’s scores around the mean in this distribution? Round your answer to two decimal places.
8. Assuming that the distribution of scores is normal, 99% of HIV-positive body image scores around the mean were between what two values? Round your answer to two decimal places.
99% of HIV-positive body image scores for males were between (24.14, 111.86):
9. Assuming that the distribution of scores for Role Functioning is normal, 99% of the men’s scores around the mean were between what values? Round your answer to two decimal places.
10. What are some limitations of this study that decrease the potential for generalizing the findings to the target population?
HLT 362V Module 3 Hypothesis Testing Week 3
Problem 1
1. There is a new drug that is used to treat leukemia. The following data represents the remission time in weeks for a random sample of 21 patients using the drug.
Problem 2
2. We wish to test the claim that the mean body mass index (BMI) of men is equal to the mean BMI of women. Use the data to the right to test this claim.
HLT 362V Module 3 Exercise 31
What are the two groups whose results are reflected by the t ratios in Tables 2 and 3?
Which t ratio in Table 2 represents the greatest relative or standardized difference between the pretest and 3 months outcomes? Is this t ratio statistically significant? Provide a rationale for your answer.
Which t ratio listed in Table 3 represents the smallest relative difference between the pretest and 3 months? Is this t ratio statistically significant? What does this result mean?
What are the assumptions for conducting a t-test for dependent groups in a study? Which of these assumptions do you think were met by this study?
Compare the 3 months and 6 months t ratios for the variable Exercise from Table 3. What is your conclusion about the long-term effect of the health-promotion intervention on Exercise in this study?
What is the smallest, significant t ratio listed in Table 2? Provide a rationale for your answer.
Why are the larger t ratios more likely to be statistically significant?
Did the health-promotion program have a statistically significant effect on Systolic blood pressure (BP) in this study? Provide a rationale for your answer.
Examine the means and standard deviations for Systolic BP at pretest, 3 months (completion of the treatment), and 6 months. What do these results indicate? Are these results clinically important? Provide a rationale for your answer.
Is this study design strong or weak? Provide a rationale for your answer.
Would you, as a health care provider, implement this intervention at your facility based on the Total Risk Score results? Provide a rationale for your answer.
HLT 362V Module 4 ANOVA Excel Worksheet
SYSTOLIC BLOOD PRESSURE IN DIFFERENT AGE GROUPS
The following table contains a random sample of 40 women partitioned into three groups:
Group 1: ages below 20
Group 2: ages 20 through 40
Group 3: ages over 40
The values in the table are the systolic blood pressure levels
The hypothesis test:
H0:u1=u2=u3
H1: at least one of the treatment means is different
Use the Excel Analysis ToolPak to create an Anova – Single Factor table. Is there sufficient evidence to support the claim that women in the different age categories have different mean blood pressure levels? Give reasons for your decision.
HLT 362V Module 4 Exercise 36
The researchers found a significant difference between the two groups (control and treatment) for change in mobility of the women with osteoarthritis (OA) over 12 weeks with the results of F(1, 22) 9.619, p 0.005. Discuss each aspect of these results.
State the null hypothesis for the Baird and Sands (2004) study that focuses on the effect of the GI with PMR treatment on patients’ mobility level. Should the null hypothesis be rejected for the difference between the two groups in change in mobility scores over 12 weeks? Provide a rationale for your answer.
The researchers stated that the participants in the intervention group reported a reduction in mobility difficulty at week 12. Was this result statistically significant, and if so at what probability?
If the researchers had set the level of significance or = 0.01, would the results of p 0.001 still be statistically significant? Provide a rationale for your answer.
If F(3, 60) 4.13, p 0.04, and = 0.01, is the result statistically significant? Provide a rationale for your answer. Would the null hypothesis be accepted or rejected?
Can ANOVA be used to test proposed relationships or predicted correlations between variables in a single group? Provide a rationale for your answer.
If a study had a result of F(2, 147) 4.56, p 0.003, how many groups were in the study, and what was the sample size?
The researchers state that the sample for their study was 28 women with a diagnosis of OA, and that 18 were randomly assigned to the intervention group and 10 were randomly assigned to the control group. Discuss the study strengths and/or weaknesses in this statement.
In your opinion, have the researchers established that guided imagery (GI) with progressive muscle relaxation (PMR) reduces pain and decreases mobility difficulties in women with OA?
The researchers stated that this was a 12-week longitudinal, randomized clinical trial pilot study with 28 women over 65 years of age with the diagnosis of OA. What are some of the possible problems or limitations that might occur with this type of study?
HLT 362V Module 5 Correlation Regression and Chi Square Excel Worksheet
SYSTOLIC AND DIASTOLIC BLOOD PRESSURE OF FEMALES
The following table represents systolic and diastolic blood pressure measurements of 40 females.
A) Use the Excel Analysis ToolPak to find the linear correlation coefficient for the systolic and diastolic measurements.
B) Use the Excel Analysis ToolPak to determine the linear regression equation that uses the systolic pressure to predict the diastolic pressure.
C) What is the best predicted value for diastolic pressure given that a woman has a systolic level of 100?
HLT 362V EXERCISE 11 Questions to be Graded
1. What demographic variables were measured at least at the interval level of measurement?
2. What statistics were used to describe the length of labor in this study? Were these appropriate?
3. What other statistic could have been used to describe the length of labor? Provide a rationale for your answer.
4. Were the distributions of scores similar for the experimental and control groups for the length of labor? Provide a rationale for your answer.
5. Were the experimental and control groups similar in their type of feeding? Provide a rationale for your answer.
6. What was the marital status mode for the subjects in the experimental and control groups? Provide both the frequency and percentage for the marital status mode for both groups.
7. Could a median be determined for the education data? If so, what would the median be for education for the experimental and the control groups? Provide a rationale for your answer.
8. Can the findings from this study be generalized to Black women? Provide a rationale for your answer.
9. If there were 32 subjects in the experimental group and 36 subjects in the control group, why is the income data only reported for 30 subjects in the experimental group and 34 subjects in the control group?
10. Was the sample for this study adequately described? Provide a rationale for your answer.
HLT 362V EXERCISE 18 Questions to be Graded
1. In comparing men and women, which group had higher body image scores? Provide a rationale for your answer.
2. Men had higher variability in weight change over the last 12 months when compared to women. Is this statement true or false? Provide a rationale for your answer.
3. What are the X_and SD values for men’s body weight ratio?
4. Assuming that the distribution of scores is normal, calculate the scores where 95% of values around the mean lie for women with weight change over the last 3 months. Round your answer to two decimal places.
5. Assuming that the distribution of body weight ratio is a normal curve, 95% of the men lie between which two values of body weight ratio around the mean? Round your answer to two decimal places.
6. Assuming that the distribution of womens’s body image scores is normal, 99% of women’s body image scores around the mean lie between what two values? Round your answer to two decimal places.
7. Assuming that the distribution is a normal curve, 99% of men were between what ages? Round your answer to two decimal places.
8. Assuming that the distribution is a normal curve, 95% of men were between what ages? Round your answer to two decimal places.
9. Did HIV-positive participants have signifi cantly higher body image scores than those with AIDS? Provide a rationale for your response.
HLT 362V Exercise 20
1. Which patient scored the highest on the preoperative CVLT Acquisition? What was his or her T score?
2. Which patient scored the lowest on postoperative CVLT Retrieval? What was this patient’s T score?
3. Did the patient in Question 2 have more of a memory performance decline than average on the CVLT Retrieval? Provide a rationale for your answer.
4. What is the mean ( ) and standard deviation (SD) for preoperative T score for CVLT Acquisition?
5. Is the preoperative Retrieval T score for Patient 5 above or below the mean for the norm of the group? Provide a rationale for your answer.
6. Assuming that the distribution of the preoperative CVLT Retrieval T scores is normal, the middle 68% of the patients had T scores between what two values?
7. Assuming that the distribution of scores for the postoperative CVLT Retrieval T scores is normal, the middle 68% of the patients had T scores between what two values?
8. The researchers state that it appears that the functional integrity of the left temporal lobe, despite evidence of structural abnormality, plays a considerable role when it comes to memory outcomes following left ATL. Can the findings from this study be generalized to a larger population? Provide a rationale for your answer.
9. If a patient had a raw score = 30, what would his/her postoperative CVLT Retrieval T score be?
10. Did patients demonstrate more postoperative memory declines among CVLT Retrieval T scores than CVLT Acquisition T scores? Provide a rationale for your answer.
HLT 362V EXERCISE 23 Questions to be Graded
1. What is the r value for the relationship between Hamstring strength index 60°/s and the Shuttle run test? Is this r value significant? Provide a rationale for your answer.
2. Consider r = 1.00 and r = -1.00. Which r value is stronger? Provide a rationale for your answer.
3. Describe the direction of the relationship between the Hamstring strength index 60°/s and the Shuttle run test.
4. Without using numbers, describe the relationship between the Hamstring strength index 120°/s and the Triple hop index.
5. Which variable has the weakest relationship with the Quadriceps strength index 120°/s? Provide a rationale for your answer.
6. Which of the following sets of variables has the strongest relationship?
a. Hamstring strength index 120°/s and the Hop index
b. Quadriceps strength index 60°/s and the Carioca test
c. Quadriceps strength index 120°/s and the Side step test
d. Quadriceps strength index 60°/s and the Triple hop index
7. In Table 5, two r values are reported as r = -0.498 and r = -0.528. Describe each r value in words, indicating which would be more statistically significant, and provide a rationale for your answer.
8. The researchers stated that the study showed a positive, significant correlation between Quadriceps strength indices and pre- and postoperative functional stability. Considering the data presented in the Table 5, do you agree with their statement? Provide a rationale for your answer.
9. The researchers stated that no significant relationship could be described between Hamstring strength indices 60°/s and functional stability. Given the data in Table 5, explain why not.
10. Consider the relationship reported for the Quadriceps strength index 120°/s and the Hop index (r = 0.744**, p = 0.000 ). What do these r and p values indicate related to statistical significance and clinical importance?
HLT 362V EXERCISE 24 Questions to be Graded 80
1. What is the r value listed for the relationship between variables 4 and 9?
2. Describe the correlation r = -0.32** using words. Is this a statistically significant correlation? Provide a rationale for your answer.
3. Calculate the percentage of variance explained for r = 0.53. Is this correlation clinically important? Provide a rationale for your answer.
4. According to Table 2, r = 0.15 is listed as the correlation between which two items? Describe this relationship. What is the effect size for this relationship, and what size sample would be needed to detect this relationship in future studies?
5. Calculate the percentage of variance explained for r = 0.15. Describe the clinical importance of this relationship.
6. Which two variables in Table 2, have the weakest correlation, or r value? Which relationship is the closest to this r value? Provide a rationale for your answer.
7. Is the correlation between LOT-R Total scores and Avoidance-Distraction coping style statistically significant? Is this relationship relevant to practice? Provide rationales for your answers.
8. Is the correlation between variables 9 and 4 significant? Is this correlation relevant to practice? Provide a rationale for your answer.
9. Consider two values, r = 0.08 and r = -0.58. Describe them in relationship to each other. Describe the clinical importance of both r values.
10. Examine the Pearson r values for LOT-R Total, which measured Optimism with the Task and Emotion Coping Styles. What do these results indicate? How might you use this information in your practice?
BONUS QUESTION
One of the study goals was to examine the relationship between optimism and psychopathology. Using the data in Table 2, formulate an opinion regarding the overall correlation between optimism and psychopathology. Provide a rationale for your answer.
HLT 362V Week 1 Discussions Questions
How could graphics and/or statistics be used to misrepresent data? Where have you seen this done? What are the characteristics of a population for which a mean/median/mode would be appropriate?
HLT 362V Week 2 Discussions Questions
Explain the importance of random sampling. What problems/limitations could prevent a truly random sampling and how can they be prevented?
How large would your population have to be for a sample to be appropriate (i.e., rather than measuring the whole population)?
HLT 362V Week 3 Discussions Questions
Suppose you hear an “old-timer” say, “Why, in my day, kids were much more respectful and didn’t cause as much trouble as they do nowadays!” Formulate a hypothesis related to this statement that you could test. How would you test it?
Researchers routinely choose an α-level of 0.05 for testing their hypotheses. What are some experiments for which you might want a lower α -level (e.g. 0.01)? What are some situations in which you might accept a higher level (e.g. 0.1)?
Explain when a z-test would be appropriate over a t-test.
Researchers routinely choose an alpha level of 0.05 for testing their hypotheses. What are some experiments for which you might want a lower alpha level (e.g., 0.01)? What are some situations in which you might accept a higher level (e.g., 0.1)?
HLT 362V Week 4 Discussions Questions
How would you explain the analysis of variance, assuming that your audience has not had a statistics class before?
What is an interaction? Describe an example; what are the variables within your population (work, social, academic, etc.) for which you might expect interactions?
HLT 362V Week 5 Discussions Questions
Now that you are familiar with the basic concepts of statistics, what are some examples of when you have seen or heard statistics used inappropriately?
Describe the error in the conclusion. Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. As the number of cigarettes increases the pulse rate increases. Conclusion: Cigarettes cause the pulse rate to increase.
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 • Task QUESTION 1 Decision Analysis Guide to marks: 20 marks- 6 for a, 2 each for b1 & b2, 3 each for b3 & b4, 4 for b5 Show all calculations to support your answers. You may follow the methods shown in the mp4 on Decision Analysis for a way to do part (b) of this question if you wish. (a) Discuss the differences among decision making under certainty, under risk and under complete uncertainty. (b) Bikram Shrestha is considering investing some money that he inherited. The following payoff matrix gives the profits that would be realised during the next year for each of the investments that Bikram is considering. Good Economy Poor Economy Share market $80,000 ($20,000) Bonds 30,000 20,000 Real estate 25,000 15,000
Answer the following questions. Each answer must be supported with appropriate calculations and/or a table of figures, and you must state for questions 1 to 4 which alternative would be selected. 1 Which alternative would an optimist choose? 2 Which alternative would a pessimist choose? 3 Which alternative is indicated by the criterion of regret? 4 Assuming probability of a good economy = 0.3 using expected monetary values what is the optimum action? 5 What is the expected value of perfect information? QUESTION 2 Value of information Guide to marks: 20 marks – 4 for a, 8 for b, 2 for c, 6 for d Show all calculations to support your answers. You may follow the methods shown in the mp4 on Value of info for a way to answer this question if you wish, but however you do the calculations you must specifically provide answers to the 4 questions. DO NOT ROUND probability calculations with Round Function. You may display them to 2 decimal places if you like but do not round in memory. Jerry is thinking about opening a bicycle shop. He can open a large shop (a1) or a small shop (a2). He believes that a large shop would earn a profit of $80,000 if the market is good (s1) but would lose $40,000 if the market is poor (s2). A small shop would return $30,000 profit in a good market and a loss of $10,000 in a poor market. Jerry believes that there is a 50-50 chance that the market will be good. (a) What should Jerry do? Show calculations. A friend would charge him $3,000 for some market research providing.one of two signals, that the market is favourable or unfavourable. His past record is such that 80% of the time he would correctly provide a favourable market prediction when the market is good and 60% of the time he would correctly provide an unfavourable market prediction when the market is poor. (b) Revise the prior probabilities in light of his friend’s track record. (c) What is the posterior probability of a good market given that his friend has provided an unfavourable market prediction? (d) What is the expected net gain or loss from engaging his friend to conduct the market research? Should his friend be engaged? Why?
QUESTION 3 Monte Carlo Simulation This is a work integrated assessment item. The tasks are similar to what would be carried out in the workplace. Guide to marks: 20 marks – 12 for a, 2 for b, 6 for c Tully Tyres sells cheap imported tyres. The manager believes its profits are in decline. You have just been hired as an analyst by the manager of Tully Tyres to investigate the expected profit over the next 12 months based on current data. • Monthly demand varies from 100 to 200 tyres – probabilities shown in the partial section of the spreadsheet below. • The average selling price per tyre follows a discrete uniform distribution ranging from $60 to $80 each. This means that it can take on equally likely integer values between $60 and $80 – more on this below. • The average profit margin per tyre after covering variable costs follows a continuous uniform distribution between 20% and 30% of the selling price. • Fixed costs per month are $1500. (a) Using Excel set up a model to simulate the next 12 months to determine the expected average monthly profit for the year. You need to have loaded the Analysis Toolpak Add-In to your version of Excel. You must keep the data separate from the model. The model should show only formulas, no numbers whatsoever. You can use this template to guide you:
Tully Tyres DATA Prob Cum prob Demand Selling Price $60 $80 0.05 100 Monthly Fixed cost $1,500 0.10 120 Profit Margin 20% 30% 0.20 140 0.30 160 0.25 180 0.10 200 1.00 MODEL Selling Profit Fixed Month RN 1 Demand Price RN 2 Margin Costs Profit
• The first random number (RN 1) is to simulate monthly demands for tyres. • The average selling price follows a discrete uniform distribution and can be determined by the function =RANDBETWEEN(60,80) in this case. But of course you will not enter (60,80) but the data cell references where they are recorded. • The second random number (RN 2) is used to help simulate the profit margin. • The average profit margin follows a continuous uniform distribution ranging between 20% and 30% and can be determined by the formula =0.2+(0.3-0.2)*the second random number (RN 2). Again you do not enter 0.2 and 0.3 but the data cell references where they are located. Note that if the random number is high, say 1, then 0.3-0.2 becomes 1 and when added to 0.2 it becomes 0.3. If the random number is low, say 0, then 0.3-0.2 becomes zero and the profit margin becomes 0.2. • Add the 12 monthly profit figures and then find the average monthly profit. Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show the grid (ie., row and column numbers) and be copied from Excel and pasted into Word. See Spreadsheet Advice in Interact Resources for guidance. (b) Provide the average monthly profit to Tully Tyres over the 12-month period.. (c) You present your findings to the manager of Tully Tyres. He thinks that with market forces he can increase the average selling price by $20 (ie range from $80 to $100) without losing sales. However he does suggest that the profit margin would then increase to range from 22% to 32%. He has suggested that you examine the effect of these changes and report the results to him. Change the data accordingly in your model to make the changes and paste the output in your Word answer Then write a report to the manager explaining your conclusions with respect to his suggestions. Also mention any reservations you might have about the change in selling prices. The report must be dated, addressed to the Manager and signed off by you. (Word limit: No more than 150 words)
QUESTION 4 Regression Analysis Guide to marks: 20 marks – 5 for a, 10 for b, 3 for c, 2 for d Belinda, the accountant at Murray Manufacturing Company wants to identify cost drivers for support overhead costs. She has the impression that the staff spend a large part of their time ensuring that the equipment is correctly set up and checking the first units of production in each batch. Deborah has collected the following data for the past 12 months: Month OH Cost MH Batches 1 $80,000 2,200 300 2 40,000 2,400 120 3 63,000 2,100 250 4 45,000 2,700 160 5 44,000 2,300 200 6 48,000 3,800 170 7 65,000 3,600 260 8 46,000 1,800 160 9 33,000 3,200 150 10 66,000 2,800 210 Total 530,000 26,900 1,980
(a) Using the high-low method to estimate support overhead costs based on machine hours, what would be the estimated support overhead costs (to the nearest $) for a month in which 3,000 machine hours were used? (b) Using Excel, perform three regression analyses to regress Overhead Cost against Machine Hours, then against Batches, then against both of them simultaneously. Paste your results into Word. State the cost equation from each. Analyse and comment on the results of each regression as you perform it and determine the best one to use as a basis for future use. (c) If you had to settle for the results of a simple regression, which one would you use and why? (d) Using the best regression result determine the projected Overhead Cost in a month in which there were 2000 machine hours worked and 150 batches produced. QUESTION 5 CVP Analysis Guide to marks: 20 marks – 4 for a, 4 for b, 4 for c, 8 for d Show all calculations to support your answers. A manufacturer can make two products, A and B. The following data are available:B Product A B Total Sales price per unit $10 $20 Variable cost per unit $5 $12 Total fixed costs $4,000
(a) Calculate the unit contribution margin for each product. (b) This month the manufacturer will specialise in making only Product B. How many does he need to sell to break even? (c) If they specialise in making only A what is the breakeven sales volume for the month in sales dollars? (d) He now decides to manufacture both A and B this month in the ratio of 2 A to 1 of B. (i) How many of each product must be sold to earn a profit of $5,000 before tax for the month? (ii) How many of each product must be sold to earn a profit of $21,000 after tax (of 30c in the dollar) for the month? END OF ASSIGNMENT 3
Rationale This assessment task covers topics 3,4,5,6 and 8: Decision analysis and value of information, simulation, correlation and regression analysis and CVP analysis. Specifically, it seeks to assess your ability to complete the following subject learning outcomes: o apply decision theory to business situations o use simulation in complex decisions o demonstrate understanding of the application of statistical hypothesis testing in regression analysis o apply CVP analysis to product mix decisions involving single and multiple
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Random Variable and Distribution Function Assignments
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