9. Hypothesis Testing for One Sample

A researcher claims that 5% of people who wear eyeglasses purchase their eyeglasses online. Describe type I and type II errors for a hypothesis test of the claim. (Source: Consumer Reports)

In Exercises 7–10, the statement represents a claim. Write its complement and state which is Ho and which is Ha.

μ<33

In Exercises 7–10, the statement represents a claim. Write its complement and state which is Ho and which is Ha.

μ≠2.28

In Exercises 3–8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance alpha and sample size n.

Left-tailed test, α=0.10, n=38

Writing You are testing a claim and incorrectly use the standard normal sampling distribution instead of the t-sampling distribution, mistaking the sample standard deviation for the population standard deviation. Does this make it more or less likely to reject the null hypothesis? Is this result the same no matter whether the test is left-tailed, right-tailed, or two-tailed? Explain your reasoning.

In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance α.

Right-tailed test, n=27,α=0.05

In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance α.

Left-tailed test, n=24,α=0.05

In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance α.

Two-tailed test, n=81,α=0.10

In Exercises 7–10, the statement represents a claim. Write its complement and state which is Ho and which is Ha.

σ=0.63

Testing the Spearman Rank Correlation Coefficient for n>30 When you are testing the significance of the Spearman rank correlation coefficient and the sample size n is greater than 30, you can use the expression below to find the critical value.

In Exercises 13 and 14, test the Spearman rank correlation coefficient

[APPLET] Work Injuries The table shows the average hours worked per week and the numbers of on-the-job injuries for a random sample of U.S. companies in a recent year. At α = =0.10, can you conclude that there is a significant correlation between average hours worked and the number of on-the-job injuries?

Runs Test with Quantitative Data In Exercises 21–23, use the following information to perform a runs test. You can also use the runs test for randomness with quantitative data. First, calculate the median. Then assign a + sign to those values above the median and a - sign to those values below the median. Ignore any values that are equal to the median. Use α = 0.05

Use technology to generate a sequence of 30 numbers from 1 to 99, inclusive. Test the claim that the sequence of numbers is not random.

Identifying a Test In Exercises 21–24, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

Ha: p = 0.25

H0: p ≠ 0.25

Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis test of the indicated claim.

Repeat Customers A used textbook selling website claims that at least 60% of its new customers will return to buy their next textbook.

Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis test of the indicated claim.

Chess A local chess club claims that the length of time to play a game has a standard deviation of more than 12 minutes.

Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.

c = 0.99, n = 15