MGMT2262 Practice Final

 

This covers material since the midterm. Of course, you should be able to solve problems from before the midterm.

 

Question 1

A company went through a merger with a major competitor. Based on 3 years’ worth of data, its average closing stock price on the TSX was $56.50. Over the following 3 months, the closing stock price was noted each Friday to see if there was any significant change. These were the results:

64.08

66.08

57.77

69.18

58.48

67.15

61.03

56.33

56.01

61.03

65.59

65.24

a)      Analysis of the data indicated it is normally distributed. Test the hypothesis at a 2% level of significance.

b)     Construct a 98% confidence interval of the average closing stock price on the TSX. Interpret the interval. If the interval were used to test the hypothesis in part a, why would the same conclusion be reached?

c)      In what range does the p-value fall? If a level of significance had not been chosen why would the same conclusion be reached?

 

Question 2

A new store conducted a survey if the percentage of people who recognized its name was greater than 10%. Of the 500 people surveyed, 60 recognized the name.

a)      Test the hypothesis at a 5% level of significance.

b)     Calculate the p-value. If the p-value is compared to the 5% level of significance, why would the same conclusion be reached?

c)      Construct a 95% confidence interval of the percentage of people who recognize the store’s name. Interpret the interval.

d)     Suppose a level of significance had not been chosen. What conclusion would be reached then?

e)      Suppose the store wanted to conduct a larger study. What would the sample size need to be if they wanted the margin of error to be no more than 1% at a 95% level of confidence using the results of the first survey?

f)       Suppose the store can afford no more than 1500 surveys. What would the margin of error be under such a scenario?

 

Question 3

A restaurant was usually slow on Tuesday and Wednesday nights. It introduced specials on these night to attract more customers. Sales are normally distributed with average daily sales of $9200 and standard deviation of $1300. A sample of 12 days of data had the following results:

7514

9508

11966

10389

10206

10040

10767

9251

8805

10947

8928

9834

a)      If the goal is to have the daily sales be more consistent, test the hypothesis at a 1% level of significance.

b)     Estimate in what range the p-value falls. If a level of significance had not been chosen, why would the same conclusion be reached?

c)      Construct a 99% confidence interval of the standard deviation of the daily sales. Interpret the interval.

d)     Suppose instead the goal was to see if average daily sales had increased. Test the hypothesis at a 1.74% level of significance.

e)      Calculate the p-value for the test in part d. For which levels of significance between 1% and 10% would the opposite conclusion have been reached?

 

Question 4

A bolts-and-nuts factory found the average cost of reworking scrap bolts into useable bolts was $43.62 per 1000 bolts with a standard deviation of $8.25. A new method of reworking the scrap bolts was tried to see if it could reduce the cost. A sample of 60 lots of 1000 scrap bolts were reworked into useable bolts at an average cost of $40.38 per lot.

a)      Test the hypothesis at a 2.87% level of significance.

b)     Calculate the p-value. Suppose a level of significance had not been chosen. Why would the same conclusion be reached?

c)      Construct a 90% confidence interval of the average cost of reworking the scrap bolts using the new method. Interpret the interval.

d)     Suppose they wanted to conduct a larger study. What would the sample size need to be if they wanted a 95% level of confidence and a margin of error of 50 cents?

e)      Suppose they cannot afford to sample more than 500 bolts at a time. What would the margin of error be under this scenario at a 95% level of confidence?