Q1. The director of a state agency believes that the average starting salary for clerical employees in the state is less than $30,000 per year. To test her hypothesis, she has collected a simple random sample of 100 starting clerical salaries from across the state and found that the sample mean is $29,750.
a. State the appropriate null and alternative hypotheses.
b. Assuming the population standard deviation is known to be $2,500 and the significance level for the test is to be 0.05, what is the critical value (stated in dollars)?
c. Referring to your answer in part b, what conclusion should be reached with respect to the null hypothesis?
d. Referring to your answer in part c, which of the two statistical errors might have been made in this case? Explain.
Q2. Starting in 2008, an increasing number of people found themselves facing mortgages that were worth more than the value of their homes. A fund manager who had investment in debt obligations involving grouped mortgages was interested in determining the group most likely to default on their mortgage. He speculates that older people are less likely to default on their mortgage and thinks the average age of those who do is 55 years. To test this, a random sample of 30 who has defaulted was selected; the following sample data reflected the ages of the sampled individuals:
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40
|
55
|
78
|
27
|
55
|
33
|
|
51
|
76
|
54
|
67
|
40
|
31
|
|
60
|
61
|
50
|
42
|
78
|
80
|
|
25
|
38
|
74
|
46
|
48
|
57
|
|
30
|
65
|
80
|
26
|
46
|
49
|
a. State the appropriate null and alternative hypotheses.
b. Use the test statistic approach to test the null hypothesis with α = 0.01.
Q3. At a recent meeting, the manager of a national call center for a major Internet bank made the statement that the average past-due amount for customers who have been called previously about their bills is now no larger than $20.00. Other bank managers at the meeting suggested that this statement may be in error and that it might be worthwhile to conduct a test to see if there is statistical support for the call center manager's statement. The file called Bank Call Center contains data for a random sample of 67 customers from the call center population. Assuming that the population standard deviation for past due amounts is known to be $60.00, what should be concluded based on the sample data? Test using α = 0.10.
Q4. A major issue facing many states is whether to legalize casino gambling. Suppose the governor of one state believes that more than 55% of the state's registered voters would favor some form of legal casino gambling. However, before backing a proposal to allow such gambling, the governor has instructed his aides to conduct a statistical test on the issue. To do this, the aides have hired a consulting firm to survey a simple random sample of 300 voters in the state. Of these 300 voters, 175 actually favored legalized gambling.
a. State the appropriate null and alternative hypotheses.
b. Assuming that a significance level of 0.05 is used, what conclusion should the governor reach based on these sample data? Discuss.
Q5. Cell phones are becoming an integral part of our daily lives. Commissioned by Motorola, a new behavioral study took researchers to nine cities worldwide from New York to London. Using a combination of personal interviews, field studies, and observation, the study identified a variety of behaviors that demonstrate the dramatic impact cell phones are having on the way people interact. The study found cell phones give people a newfound personal power, enabling unprecedented mobility and allowing them to conduct their business on the go. Interesting enough, gender differences can be found in phone use. Women see their cell phone as a means of expression and social communication, whereas males tend to use it as an interactive toy. A cell phone industry spokesman stated that half of all cell phones in use are registered to females.
a. State the appropriate null and alternative hypotheses for testing the industry claim.
b. Based on the random sample of cell phone owners shown in the data file called Cell Phone Survey, test the null hypothesis. (Use α = 0.05.)
Q6. Construct a 95% confident interval estimate for the different between two population means based on the following information:
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Population 1
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Population 2
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x-1 = 355
|
x-2 = 320
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|
σ1 = 34
|
σ2 = 40
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|
n1 = 50
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n2 = 80
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Q7. Wilson Construction and Concrete Company is knows as a very progressive company that is willing to try new ideas to improve its products and service. One of the key factors of importance in concrete work is the time it takes for the concrete to "set up." The company is considering a new additive that can be put in the concrete mix to help reduce the setup time. Before going ahead with the additive, the company plans to test it against the current additive. To do this, 14 batches of concrete are mixed using each of the additives. The following results were observed:
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Old Additive
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New Additive
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x- = 17.2 hours
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x- = 15.9 hours
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s = 2.5 hours
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s = 1.8 hours
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a. Use these sample data to construct a 90% confidence interval estimate for the difference in mean setup time for the two concrete additives. On the basis of the confidence interval produced, do you agree that the new additive helps reduce the setup time for cement? (Assume the populations normally distributed.) Explain your answer.
b. Assuming that the new additive is slightly more, expensive than the old additive, do the data support switching to the new additive if the managers of the company are primarily interested in reducing average setup time?
Q8. The marketing manager for a major retail grocery chain is wondering about the location of the stores' dairy products. She believes that the mean amount spent by customers on dairy products per visit is higher in stores in which the dairy section is in the central part of the store compared with stores that have the dairy section at the rear of the store. To consider relocating the dairy products, the manager feels that the increase in the mean amount spent by customers must be at least 25 cents. To determine whether relocation is justified, her staff selected a random sample of 25 customers at stores in which the dairy section is central in the store. A second sample of 25 customers was selected in the stores with the dairy section at the rear of the store. The following sample results were observed:
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Central Dairy
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Rear Dairy
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x-1 = $3.74
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x-2 = $3.26
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s1 = $0.87
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s2 = $0.79
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a. Conduct a hypothesis test with a significant level of 0.05 to determine if the manager should relocate the dairy products in those stores displaying their dairy products in the rear of the store.
b. If a statistical error associated with hypothesis testing was made in this hypothesis test, what error could it have been? Explain.