SCHULICH SCHOOL OF BUSINESS YORK UNIVERSITY SESSION ...s3.amazonaws.com/prealliance_oneclass_sample/0x9kOb94v8.pdf · the standard deviation of the width being less than 0.85mm. A

SCHULICH SCHOOL OF BUSINESSYORK UNIVERSITY

SESSION: Practice Final Exam NAME:

COURSE NO: MGMT 10 5 0 I.D. # :

COURSE TITLE: Statistics for Management SECTION:

PROFESSORS:

NUMBER OF PAGES: 13 pages (NOT including cover) LENGTH OF EXAMINATION: 150 minutesEXAMINATION AIDS ALLOWED: Calculator; Formula and Tables Book

INSTRUCTIONS:

1. Please place your I.D. card on your desk.

2. You are not allowed to leave the examination room until one hour after the start of the exam and you must sign the sign-in sheet before leaving.

3. Your examination paper must be handed in before you leave. When you are finished please leave the exam room quietly.

4. Cheating on an examination will result in an “F” grade in the course concerned and possible suspension from the University.

5. All notes, briefcases, and books must be deposited at the front of the room.

6. You are not allowed to use your own paper for rough work. You may only use the space provided or the back of the pages for rough work.

7. Answer the Multiple Choice and True/False Questions on the Scantron Sheet supplied. Be sure to put your name and student number on the bubble sheet. In Parts I and IV, place your answers in the answer boxes, where supplied.

8. Count the pages to be certain that there are no pages missing.

9. Do not remove the staple or any pages from the exam.

10. Please show all your work.

11. If alpha is not given in the question use 0.05

12. Do not begin this examination until you are instructed to do so.

13. Do not write in the mark summary table below.

Part I – Problem Recognition 24 marks

Part II – True/False 8 marks

Part III – Multiple Choice Questions 10 marks

Part IV – Problems Question 1 8 marks

Question 2 22 marks

Question 3 20 marks

Question 4 8 marks

Sub-total 58 marks

TOTAL 100 marks

MGMT1050 Practice Final Examination

PART I - PROBLEM RECOGNITION (24 MARKS, 2 MARKS EACH)

Instructions: For each of the scenarios below, write the null and alternative hypotheses and indicate the most appropriate statistical test. You are not required to conduct the test, just choose the most suitable test from the following options: z-test; t-test; χ2-test; F-test, ANOVA.

Notes: (1) Be specific in your answers: for example, specify the type of ANOVA required (one-way,

randomized block, or two-way), or whether you would use the t-test for equal variances or not. (2) When writing hypotheses for two population tests, use meaningful indexing. For example, if the

question asks to compare Canada and the US, write µc-µu as opposed to µ1-µ2. (3) Write all relevant hypotheses for each of the questions.

1.

Do “captive stores” price differently than independent retailers? In order to test this question, a researcher selected 20 Sony products and collected the prices for these items at three stores: the “Sony Style” store, “The Source” and a local electronics retailer.

Hypotheses (H0 and HA):

Test:

2.

Clothes lines, where people hang their clothes outside on lines to dry, are making a come-back as people strive to reduce the amount of energy used. One green consumer who had both types of clothes lines (the pulley type and the collapsible clothes line tree style) decided to see if there is a deference in drying times by splitting the clothes to be dried evenly by type between the two types of clothes lines for 15 weeks.


Test:

3.

An accounting student, trying to determine her optimal career path, want to see how the incomes of accountants varied based on which designation they held (CA, CMA, CGA) and whether they worked in industry or private practice.


Test:

4.

Has the recent decline in the stock market affected investor’s retirement portfolios? A study three years ago found that for families with the oldest working spouse between 50 and 60 years old, the average portfolio value was $325,000. A survey of 200 families in the same age group done last month found the average to be $275,000 with a standard deviation of $65,000.


Test:

DO NOT REMOVE THE STAPLE OR ANY PAGES Page 2 of 15


5.

A quality control inspector wants to see is a new supplier is providing castings within the requirement of the standard deviation of the width being less than 0.85mm. A sample of 60 castings found the variance to be 0.6561mm2.


Test:

6.

There has been controversy about the effectiveness of the national Do Not Call (DNC) List. In fact, many people are complaining that they are getting more calls now that they have registered for the DNC List. A researcher obtained clearance from 200 randomly selected people on the DNC List to get access to their telephone records to compare how many call they received in September, prior to the implementation of the DNC List, and January, after registration for the DNC List.


Test:

7.

Does choice of business school affect the choice of major or concentration? To test this, a researcher took random samples of 100 graduating students from (1) Schulich, (2) Ivey, and (3) Laurier and categorized then by the following majors: (A) Accounting, (B) Marketing, (C) Finance, (D) International, (E) OB/HR and (F) Other.


Test:

8.

Suppose that the study in question 7 only compared Schulich and Ivey.


Test:



9.

Suppose that the study in question 7 also looked at whether the starting salaries offered to the graduating students were affected by the school and major.


Test:

10.

Load management is important to maximize the revenue of airlines. One practice that most airlines use is overbooking. According to one industry source, the probability that an individual shows up for their flight is 90%. Therefore, the number of people showing up should be distributed with a binomial distribution. A statistical analyst with an airline accesses company records to see how many people actually showed up for their flights when exactly 300 people were booked. This has happened 1225 times in the past year.


Test:

11.

According to a major study of traffic on highway 401 done 4 years ago, the standard deviation of the speed of vehicles was 13.4kph. With the recent introduction of speed limiters on large trucks, there is concern that there will be more variability of speeds. Two-thousand vehicles are sampled on days with clear weather and dry road conditions.


Test:

12.

A major office supply cost for large firms is toner in printers. To see if a new line of “ECO” printers saves toner, 200 workstations equipped with the standard printer used by the firm were randomly selected and half of these had their printer replaced with the “ECO” line printer. The toner usage was measured for one month.


Test:



PART II – TRUE/FALSE (8 MARKS, 1 MARK EACH)

Instructions: Indicate whether the following statements are true or false on the Scantron Sheet provided, starting at #1. Use "A" for True and use "B" for False. There will be no deduction for an incorrect answer.

1. In a two-way ANOVA, it is easier to interpret main effects when the interaction component is not significant.

2. When the F test is used for ANOVA, the rejection region is always in the right tail.

3. The F test used for testing the difference in 2 population variances is always a one-tailed test.

4. The larger the p value, the more likely one is to reject the null hypothesis.

5. For a given level of significance, if the sample size is increased, the probability of committing a Type I error will increase.

6. Suppose, in testing a hypothesis about a proportion, the Z test statistic is computed to be 2.04. The null hypothesis should be rejected if the chosen level of significance is 0.01 and a two-tailed test is used.

7. The t distribution allows the calculation of confidence intervals for means for small samples when the population variance is not known, regardless of the shape of the distribution in the population.

8. The confidence interval obtained will always correctly estimate the population parameter.



PART III – MULTIPLE CHOICE QUESTIONS (10 MARKS, 1 MARK EACH)

Instructions: Answer each question below on the Scantron Sheet provided (start from question 9). There is only one best answer. There is no penalty for guessing.

9 The width of a confidence interval estimate for a proportion will beA. Narrower when the sample proportion is 0.50 than when the sample proportion is

0.20B. Wider for a sample size of 100 than for a sample size of 50C. Narrower for 99% confidence than for 95% confidenceD. Narrower for 90% confidence than for 95% confidence

10 If we wish to determine whether there is evidence that the proportion of successes is the same in group 1 as in group 2, the appropriate test to use is

A. The χ2 testB. The Z testC. Both of the aboveD. None of the above

11 In testing a hypothesis using the χ2 test, the theoretical frequencies are based on the

A. Alternative hypothesisB. Null hypothesisC. Normal distributionD. None of the above

12 The t test for the difference between the means of 2 independent populations assumes that the respective

A. Sample variances are equalB. Populations are approximately normalC. Sample sizes are equalD. None of the above

13 A confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Based on the interval above, is the population proportion of females equal to 0.60?

A. Yes, and we are 90% sure of itB. No, and we are 90% sure of itC. No. The proportion is 54.17%D. Maybe. 0.60 is a believable value of the population proportion based on the

information above

14 A Type I error is committed whenA. We reject a null hypothesis that is trueB. We don't reject a null hypothesis that is trueC. We don't reject a null hypothesis that is falseD. We reject a null hypothesis that is false



15 Suppose we wish to test H0: μ ≤ 47 versus H1: μ > 47. What will result if we conclude that the mean is greater than 47 when its true value is really 52?

A. We have made a Type II errorB. We have made a Type I errorC. We have made a correct decisionD. None of the above are correct

16 Which of the following would be an appropriate alternative hypothesis?A. The mean of a sample is greater than 55B. The mean of a sample is equal to 55C. The mean of a population is greater than 55D. The mean of a population is equal to 55

17 As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. Which of the following assumptions is necessary in order for a confidence interval to be valid?

A. The mean of the sample equals the mean of the populationB. The population sampled from has an approximate t distributionC. The population sampled from has an approximate normal distributionD. None of these assumptions are necessary

18 A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the average owed is $83.40 with a sample standard deviation of $23.65. What test would you use?

A. χ2 test of population varianceB. Z-test of a population meanC. t-test of a population meanD. Z-test of a population proportion



PART IV – PROBLEMS (58 MARKS)

Question 1 (8 Marks)

A major home improvement store conducted its biggest brand recognition campaign in the company's history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot". A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad at a 0.01 level of significance.

a. State the null and alternative hypotheses for this study. (1 mark)

Null Hypothesis Alternative Hypothesis

b. What critical value should the company officials use to determine the rejection region? (1 mark)

Answer:

c. The null hypothesis will be rejected if the test statistics is greater than/less than (choose one)

negative/positive (choose one) _____________ (insert value). (1 mark)

d. What is your conclusion? (3 marks)

Answer:

e. What is the lowest level of significance at which the null hypothesis can be rejected? (1 mark)

Answer:

f. What will be the p-value if these data were used to perform a two-tailed test? (1 mark)

Answer:



Question 2 (22 marks)

A consumer group wants to see if shopping at the discount affiliate of a major grocery chain saves money. However, before sampling specific items, they randomly sampled six customers at each type of store. The data collected is presented in the table below, with some summary statistics presented. The consumer group believes that the data are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.

Grocery Chain

Discount Affiliate

$55 $45$48 $47$31 $32$83 $77$37 $37$55 $54

Sum: $309 $292Sum of Squares: $17,573 $15,472

a. Test the consumer group’s conjecture using a significance level of .01. (8 marks)

Answer:

b. The p-value of the test is (1 mark):



Question 2 (Continued)

c. Would your answer change if the items purchased by customers sampled were the same, i.e., the first customers surveyed from each store purchased the same items, as the second, etc.? If no, explain. If yes, how would it change (show your calculations)? (5 Marks)

Answer

d. Referring to the problem described in part c, if the buyer had decided to perform a two-tailed

test, the p-value would have been between __________ and ____________. (2 marks)

e. What is the 95% confidence interval estimate for the mean difference in prices? (3 marks)

Answer LCL: UCL:

Show work here:

f. If the buyer wanted to estimate the confidence interval for the mean differences within $3, how many more prices for different materials should he had been collected? (3 marks)

Answer How many more:

Show work here:




Specific Motors has been analyzing the quality of an electrical component that is supplied by three different suppliers. The installation method also differs due to which of three assembly methods are used. An α = 5% was used. The following is the partial ANOVA output:

ANOVASource of Variation SS df MS F F-Crit

Rows (Supplier) 836.2889

Columns (Method) 858.1556

Interaction 91.91111

W ithin 10287.3

Total 12073.66 89

a. State the appropriate null and alternate hypotheses. (4 marks)

Answer:

b. How many replicates are there in the analysis? (1 mark)

Answer:

c. Fill in the missing values in the ANOVA output in the table above. (8 marks)

d. What do you conclude from performing the hypothesis tests? (2 marks)

Answer:



Question 3 (Continued)

e. Irrespective of the results that you obtained in part (d), assume that only the variable “Method” has a significant impact on quality. Create the appropriate ANOVA table in the grid below: (5 marks)

ANOVASource of Variation SS df MS F F-Crit

Total




Suppose that an analyst at Specific Motors examined the number of unacceptable quality components and found the following:

Supp A Supp B Supp CMethod X 13 4 7Method Y 5 9 6Method Z 6 7 7

Required:

Is there evidence at α = 10% that the installation method and supplier are related in terms of the number of unacceptable quality components? Show all the appropriate steps.



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EXTRA FORMULAE:

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SCHULICH SCHOOL OF BUSINESS YORK UNIVERSITY SESSION ...s3.amazonaws.com/prealliance_oneclass_sample/0x9kOb94v8.pdf · the standard deviation of the width being less than 0.85mm. A