MGMT2263 Midterm practice questions

ITEM 1

The Richard Manufacturing Company produces custom wooden crates that are sold to shipping companies worldwide. Each crate is assembled by skilled line-operators. Each operator is expected to produce, on the average, the same number of finished units per day. Data for two operators was collected for a period of a week (6 days total) and resulted in the following data.

Day	Operator 1	Operator 2
Monday	108	106
Tuesday	115	118
Wednesday	118	116
Thursday	116	115
Friday	110	114
Saturday	115	112

a) Assume the population data is normally distributed. At a 5% level of significance, can we conclude that the operators differ in their job-performance? Conduct the required test of hypothesis.

b) Manually calculate a 95% confidence interval estimate for the mean difference in production output for the two operators. Does this interval support the test result reached in part a)? State why.

c) If you could no longer assume that the population-mean-difference was normally distributed, conduct the appropriate non-parametric test procedure to address the same issue as outlined in part a). Once again, use a 5% level of significance to conduct your test.

ITEM 2

A manufacturer of camping equipment is designing a new line of tents. Four different suppliers are being considered for supplying the fabric that will go into the tents. A test on the tensile strength of the fabric coming from each supplier is conducted and resulted in the following data.

Supplier 1	Supplier 2	Supplier 3	Supplier 4
18.5	26.3	20.6	25.4
24.0	25.3	25.2	19.9
17.2	24.0	20.8	22.6
19.9	21.2	24.7	17.5
18.0	24.5	22.9	20.4

a) Complete the following ANOVA table for this problem.

Source	df	SS	MS	F-stat
Total

b) Can we conclude whether or not the population variances differ? Conduct the required test of hypothesis using a 5% level of significance. Based on the conclusion of this test, is it appropriate to conduct ANOVA? Discuss briefly.

c) Is the mean tensile strength different amongst the four suppliers? Conduct the required test of hypothesis using a 5% level of significance.

d) Is Tukey’s assessment useful? Base your answer on your conclusion reached in part c). If you conclude that this assessment is useful, which means are significantly different using a 5% level of significance?

e) Calculate a 95% confidence interval for the difference in mean tensile strength between the fabric from Supplier #2 and Supplier #3.

ITEM 3

A study is being conducted by a major marketing research firm with regard to the number of full-page advertisements run in nationally circulated monthly magazines. They are particularly interested in two of these magazines, A and B. A random sample of monthly issues was selected and the number of full-page ads was counted and resulted in the following data.

A	17	26	18	16	15	23	20
B	8	9	24	12	10

a) Assuming the data is normally distributed, is there any difference between the population variances of the two magazines? Conduct the required test of hypothesis at a 5% level of significance.

b) Based on the results of part a), what specific means difference test should be conducted? Explain your answer briefly but do not conduct the test at this point.

c) Using the test outlined in part b), conduct the required test of hypothesis to assess if there is a difference in the mean number of full-page ads in the two magazines. Assume no level of significance in conducting your test.

d) Would your test conclusion change in part c) if you had used a 1% level of significance to conduct the test? Discuss why or why not.

e) Calculate a 95% confidence interval for the difference in the mean number of full-page ads in the two magazines.

ITEM 4

Reconsider the problem setup and the data from ITEM 3.

A study is being conducted by a major marketing research firm with regard to the number of full-page advertisements run in nationally circulated monthly magazines. They are particularly interested in two of these magazines, A and B. A random sample of monthly issues was selected and the number of full-page ads was counted and resulted in the following data.

A	17	26	18	16	15	23	20
B	8	9	24	12	10

a) If the data can no longer be considered to have been drawn from normally distributed populations, what non-parametric test should be conducted in order to address the question of whether or not the volume of full-page ads differ between the two magazines? Briefly explain.

b) Using the test method outlined in part a), conduct the required non-parametric analysis. Use a 5% level of significance in the test.

ITEM 5

A marketing research analyst has been hired by a major consumer electronics manufacturer to study the difference in age usage of MP3 systems. The two groups studied were those 25 years old and younger and those over 25 years of age. In the group of individuals 25 years and younger a sample of 1200 individuals were surveyed and 900 expressed that they used an MP3 system on a regular basis. The group of individuals that were over 25 years of age was made up of 1500 individuals and 900 of them expressed that they used an MP3 system on a regular basis. Using this information answer the following questions.

a) Can we conclude that there is more than a 10% greater usage of MP3 systems in the 25 year old or younger group when compared to the over 25 year age group? Conduct the required test of hypothesis using a 5% level of significance.

b) Estimate a P-value for the test conducted in part a). Does this value support the test outcome reached in part a)? Discuss briefly.

c) Calculate a 95% confidence interval estimate for the difference in rates of MP3 usage between the two groups.