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Chapter 9: Problem 9

Write the null and alternative hypotheses for each of the following examples. Determine if each is a case of a two-tailed, a left-tailed, or a right-tailed test. a. To test if the mean number of hours spent working per week by college students who hold jobs is different from 20 hours b. To test whether or not a bank's ATM is out of service for an average of more than 10 hours per month c. To test if the mean length of experience of airport security guards is different from 3 years d. To test if the mean credit card debt of college seniors is less than \(\$ 1000\) e. To test if the mean time a customer has to wait on the phone to speak to a representative of a mailorder company about unsatisfactory service is more than 12 minutes

Short Answer

Expert verified
a. Null Hypothesis: \(H_0: \mu = 20\), Alternative Hypothesis: \(H_1: \mu \neq 20\) , two-tailed test. b. Null Hypothesis: \(H_0: \mu = 10\), Alternative Hypothesis: \(H_1: \mu > 10\) , right-tailed test. c. Null Hypothesis: \(H_0: \mu = 3\), Alternative Hypothesis: \(H_1: \mu \neq 3\) , two-tailed test. d. Null Hypothesis: \(H_0: \mu = 1000\), Alternative Hypothesis: \(H_1: \mu < 1000\), left-tailed test. e. Null Hypothesis: \(H_0: \mu = 12\), Alternative Hypothesis: \(H_1: \mu > 12\), right-tailed test.

Step by step solution

01

Identifying Hypotheses and Test for Scenario a

Null Hypothesis (H0): The mean hours spent working per week by college students who hold jobs is 20 hours. \(H_0: \mu = 20\) . Alternative Hypothesis (H1): The mean hours spent working per week by college students who hold jobs is not 20 hours. \(H_1: \mu \neq 20\). This case is a two-tailed test since the alternative hypothesis is about being different, not more or less.
02

Identifying Hypotheses and Test for Scenario b

Null Hypothesis (H0): The average hours a bank's ATM is out of service per month equals 10 hours. \(H_0: \mu = 10\). Alternative Hypothesis (H1): The average hours a bank's ATM is out of service per month is more than 10 hours. \(H_1: \mu > 10\). This is a right-tailed test as the alternative hypothesis encompasses values greater than the stated value.
03

Identifying Hypotheses and Test for Scenario c

Null Hypothesis (H0): The mean length of experience of airport security guards is 3 years. \(H_0: \mu = 3\). Alternative Hypothesis (H1): The mean length of experience of airport security guards is not 3 years. \(H_1: \mu \neq 3\). This scenario represents a two-tailed test because the alternative hypothesis considers the mean different from the stated value without a specific direction.
04

Identifying Hypotheses and Test for Scenario d

Null Hypothesis (H0): The mean credit card debt of college seniors is 1000 dollars. \(H_0: \mu = 1000\). Alternative Hypothesis (H1): The mean credit card debt of college seniors is less than 1000 dollars. \(H_1: \mu < 1000\). This scenario represents a left-tailed test since the alternative hypothesis contains values that are less than the stated value.
05

Identifying Hypotheses and Test for Scenario e

Null Hypothesis (H0): The mean wait time for a customer on the phone to speak to a mailorder company's representative about unsatisfactory service is 12 minutes. \(H_0: \mu = 12\). Alternative Hypothesis (H1): The mean wait time for a customer on the phone to speak to a mailorder company's representative about unsatisfactory service is more than 12 minutes. \(H_1: \mu > 12\). This is a right-tailed test as the alternative hypothesis contains values that exceed the stated value.

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Most popular questions from this chapter

For each of the following examples of tests of hypothesis about the population proportion, show the rejection and nonrejection regions on the graph of the sampling distribution of the sample proportion. a. A two-tailed test with \(\alpha=.05\) b. A left-tailed test with \(\alpha=.02\) c. A right-tailed test with \(\alpha=.025\)

A tool manufacturing company claims that its top-of-the-line machine that is used to manufacture bolts produces an average of 88 or more bolts per hour. A company that is interested in buying this machine wants to check this claim. Suppose you are asked to conduct this test. Briefly explain how you would do so when \(\sigma\) is not known.

According to a book published in \(2011,45 \%\) of the undergraduate students in the United States show almost no gain in learning in their first 2 years of college (Richard Arum et al., Academically Adrift, University of Chicago Press, Chicago, 2011 ). A recent sample of 1500 undergraduate students showed that this percentage is \(38 \%\). Can you reject the null hypothesis at a \(1 \%\) significance level in favor of the alternative that the percentage of undergraduate students in the United States who show almost no gain in learning in their first 2 years of college is currently lower than \(45 \%\) ? Use both the \(p\) -value and the critical-value approaches.

The manager of a restaurant in a large city claims that waiters working in all restaurants in his city eart an average of \(\$ 150\) or more in tips per week. A random sample of 25 waiters selected from restaurants of this city yielded a mean of \(\$ 139\) in tips per week with a standard deviation of \(\$ 28\). Assume that the weekly tips for all waiters in this city have a normal distribution a. Using a \(1 \%\) significance level, can you conclude that the manager's claim is true? Use both approaches b. What is the Type I error in this exercise? Explain. What is the probability of making such an error'

Find the \(p\) -value for each of the following hypothesis tests. a. \(H_{0}: \mu=23, \quad H_{1}: \mu \neq 23, \quad n=50, \quad \bar{x}=21.25, \quad \sigma=5\) b. \(H_{0}: \mu=15, \quad H_{1}: \mu<15, \quad n=80, \quad \bar{x}=13.25, \quad \sigma=5.5\) c. \(H_{0}: \mu=38, \quad H_{1}: \mu>38, \quad n=35, \quad \bar{x}=40.25, \quad \sigma=7.2\)
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