9. Hypothesis Testing for One Sample

In Exercises 13–18, test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.

Claim: μ≥8000; α=0.01. Sample statistics: x_bar=77,000, s=450, n=25

In Exercises 13–18, test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.

Claim: μ=4915; α=0.01. Sample statistics: x_bar=5017, s=5613, n=51

In Exercises 13–18, test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.

Claim: μ≠52,200; α=0.05. Sample statistics: x_bar=53,220, s=2700, n=34

Hypothesis Testing Using Rejection Regions In Exercises 19–26, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic t, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed.

Credit Card Debt A credit reporting agency claims that the mean credit card debt in Colorado is greater than $5540 per borrower. You want to test this claim. You find that a random sample of 30 borrowers has a mean credit card debt of $5594 per person and a standard deviation of $597 per person. At , can you support the claim α=0.05?

Hypothesis Testing Using Rejection Regions In Exercises 19–26, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic t, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed.

Lead Levels As part of your work for an environmental awareness group, you want to test a claim that the mean amount of lead in the air in U.S. cities is less than 0.032 microgram per cubic meter. You find that the mean amount of lead in the air for a random sample of 56 U.S. cities is 0.021 microgram per cubic meter and the standard deviation is 0.034 microgram per cubic meter. At α=0.01, can you support the claim?

Hypothesis Testing Using Rejection Regions In Exercises 19–26, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic t, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed.

Annual Salary An employment information service claims the mean annual salary for senior level statisticians is more than $124,000. The annual salaries (in dollars) for a random sample of 12 senior level statisticians are shown in the table at the left. At α=0.01, is there enough evidence to support the claim that the mean salary is more than $124,000?

Dive Duration An oceanographer claims that the mean dive duration of a North Atlantic right whale is 11.5 minutes. A random sample of 34 dive durations has a mean of 12.2 minutes and a standard deviation of 2.2 minutes. Is there enough evidence to reject the claim at α=0.10?

Faculty Classroom Hours The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table at the left. At α=0.01, can you reject the dean’s claim?

Deciding on a Distribution In Exercises 31 and 32, decide whether you should use the standard normal sampling distribution or a t-sampling distribution to perform the hypothesis test. Justify your decision. Then use the distribution to test the claim. Write a short paragraph about the results of the test and what you can conclude about the claim.

Tuition and Fees An education publication claims that the mean in-state tuition and fees at public four-year institutions by state is more than $10,500 per year. A random sample of 30 states has a mean in-state tuition and fees at public four-year institutions of $10,931 per year. Assume the population standard deviation is $2380. At α=0.01, test the publication’s claim.

[APPLET] The annual earnings (in dollars) for 30 randomly selected locksmiths are shown below. Assume the population is normally distributed. (Adapted from Salary.com)

48,69446,85642,91261,67271,11254,861

69,45471,84159,75169,61254,28452,166

66,36048,16465,27235,25061,12765,397

58,92558,91659,01753,07045,19969,941

69,49257,08553,82952,69268,29853,792

A researcher claims that the mean annual earnings for locksmiths is $55,000. At α=0.05, can you reject the researcher’s claim? Interpret the decision in the context of the original claim.

A hat company claims that the mean hat size for a male is at least 7.25. A random sample of 12 hat sizes has a mean of 7.15. At α=0.01, can you reject the company’s claim? Assume the population is normally distributed and the population standard deviation is 0.27.

A travel analyst claims the mean daily base price for renting a full-size or less expensive vehicle in Vancouver, British Columbia, is more than $86. You want to test this claim. In a random sample of 40 full-size or less expensive vehicles available to rent in Vancouver, British Columbia, the mean daily base price is $93.23. Assume the population standard deviation is $28.90. At α=0.10, do you have enough evidence to support the analyst’s claim?

A government agency reports that the mean amount of earnings for full-time workers ages 18 to 24 with a bachelor’s degree in a recent year is $52,133. In a random sample of 15 full-time workers ages 18 to 24 with a bachelor’s degree, the mean amount of earnings is $48,400 and the standard deviation is $6679. At α=0.05, is there enough evidence to reject the claim? Assume the population is normally distributed.

[APPLET] A weight loss program claims that program participants have a mean weight loss of at least 10.5 pounds after 1 month. The weight losses after 1 month (in pounds) of a random sample of 40 program participants are listed below. At α=0.01, is there enough evidence to reject the program’s claim?

In Exercises 7–10, (d) explain how you should interpret a decision that rejects the null hypothesis.

An energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25.