- [10 marks] CCN and ActMedia provided a television channel targeted to individuals waiting
in supermarket checkout lines. The channel showed news, short features, and
advertisements. The length of the program assumed that the population mean time a shopper
stands in a supermarket checkout line is 8 minutes. A sample of actual waiting times will be
used to test this assumption and determine whether actual mean waiting time differs from this
standard.
a. [2 marks]Formulate the hypotheses for this application. (Include a word
description.)
b. [3 marks]A sample of 120 shoppers showed a sample mean waiting time of 8.4
minutes. Assume a population standard deviation of σ = 3.2 minutes. What is the pvalue?
c. [2 marks]At α = 0.05, what is your conclusion?
d. [3 marks]Compute a 95% confidence interval for the population mean. Does it
support your conclusion? Explain.
.
MGSC2207 Summer Session I 2021
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- [8 marks] In 2019, 46% of business owners gave a holiday gift to their employees. A
2020 survey of business owners indicated that 35% planned to provide a holiday gift to
their employees. Suppose the survey results are based on a sample of 60 business
owners.
a. [1 mark] How many business owners in the survey planned to provide a holiday gift to
their employees in 2020?
b. [5 marks] Suppose the business owners in the sample did as they planned. Compute the pvalue for a hypothesis test that can be used to determine if the proportion of business
owners providing holiday gift had decreased from the 2019 level.
c. [2 marks] Using a 0.05 level of significance, would you conclude that the proportion of
business owners providing gifts decreased? What is the smallest level of significance for
which you could draw such a conclusion?
MGSC2207 Summer Session I 2021
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- [8] Mutual funds are classified as load or no-load funds. Load funds require an investor to
pay an initial fee based on a percentage of the amount invested in the fund. The no load
funds do not require this initial fee. Some financial advisors argue that the load mutual
funds may be worth the extra fee becaise these funds provide a higher mean rate of return
than the no-load mutual funds. A sample of 30 load and 30 no-load funds were selected.
Data were collected on the annual return for the funds over a five-year period. The data
are contained in the data set Mutual. Conduct an appropriate hypothesis test to
determinewhether the load funds have a higher mean annual return over the five-year
period. Include the error you might be committing. MGSC2207 Summer Session I 2021
Page 5 of 9 - [3] Suppose that it is generally accepted that the variance in returns for the Mutual
question is considered equal for no-load and load funds. Redo your calculations as
necessary. MGSC2207 Summer Session I 2021
Page 6 of 9 - [10] A large automobile insurance company selected samples of single and married male
policy-holders and recorded the number who made an insurance claim over the preeding
three-year period.
Male Policy Holders: Single Married
Sample size 400 900
No. Making claims 76 90
a. [7] Conduct a hypothesis test to determine whether there is a difference in
proportion of claims between single and married male policy holders. Use a 0.05 level
of significance
b. [3 marks – 2 for calculations; 1 for statement] Provide a 95% confidence interval for
the difference between the proportions for the two populations.
MGSC2207 Summer Session I 2021
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- [10] A city wants to know if a new advertising campaign to make citizens aware of the
dangers of driving after drinking has been effective. It counts the number of drivers who
have been stopped with more alcohol in their systems than the month after the campaign
starts. The results are:
Day of
Week
Before After
Monday 5 2
Tuesday 4 0
Wednesday 2 2
Thursday 4 1
Friday 6 8
Saturday 14 7
Sunday 6 7
Assume a significance level of 0.05. MGSC2207 Summer Session I 2021
Page 8 of 9 - [11] Suppose now that we also have data on the number of claims by male retirees. The data
are now:
Male policy holders: Single Married Retirees
No. Making claims 76 90 45
Sample size 400 900 250
a.[7] Assume that the three categories are mutually exclusive. Using a 0.05 significance
level and a critical value approach, conduct an appropriate test to determine if there is
a significant difference in the proportion of claims among the three groups. MGSC2207 Summer Session I 2021
Page 9 of 9
b. [4] If a significant difference is determined among the three groups making claims, conduct
an appropriate test to determine where the significant differences lie.