9. Hypothesis Testing for One Sample

Right-Tailed, Left-Tailed, Two-Tailed Is the hypothesis test described in Exercise 1 right-tailed, left-tailed, or two-tailed? Explain your choice.

Ghosts The following table summarizes results from a Pew Research Center survey in which subjects were asked whether they had seen or been in the presence of a ghost. Use a 0.01 significance level to test the claim that gender is independent of response. Does the conclusion change if the significance level is changed to 0.05?

Accuracy of Fingerprint Identifications An experiment was conducted to compare the accuracy of fingerprint experts to the accuracy of novices (based on data from “Identifying Fingerprint Expertise,” by Tangen, Thompson, and McCarthy, Psychological Science, Vol. 22, No. 8). The data in the table are based on trials in which the evaluators were given matching fingerprints. Use a 0.05 significance level to determine whether correct identification is independent of whether the evaluator is an expert or a novice.

Gender and Eye Color The following table describes the distribution of eye colors reported by male and female statistics students (based on data from “Does Eye Color Depend on Gender? It Might Depend on Who or How You Ask,” by Froelich and Stephenson, Journal of Statistics Education, Vol. 21, No. 2). Is there sufficient evidence to warrant rejection of the belief that gender and eye color are independent traits? Use a 0.01 significance level.

Clinical Trial of Echinacea In a clinical trial of the effectiveness of echinacea for preventing colds, the results in the table below were obtained (based on data from “An Evaluation of Echinacea Angustifolia in Experimental Rhinovirus Infections,” by Turner et al., New England Journal of Medicine, Vol. 353, No. 4). Use a 0.05 significance level to test the claim that getting a cold is independent of the treatment group. What do the results suggest about the effectiveness of echinacea as a prevention against colds?

Equivalent Tests A x^2 test involving a 2 x 2 table is equivalent to the test for the difference between two proportions, as described in Section 9-1. Using Table 11-1 from the Chapter Problem, verify that the x^2 test statistic and the z test statistic (found from the test of equality of two proportions) are related as follows: z^2 = x^2 Also show that the critical values have that same relationship.

Robust What does it mean when we say that the F test described in this section is not robust against departures from normality?

Exercises 1–5 refer to the sample data in the following table, which summarizes the frequencies of 500 digits randomly generated by Statdisk. Assume that we want to use a 0.05 significance level to test the claim that Statdisk generates the digits in a way that they are equally likely.

What are the null and alternative hypotheses corresponding to the stated claim?

Exercises 1–5 refer to the sample data in the following table, which summarizes the frequencies of 500 digits randomly generated by Statdisk. Assume that we want to use a 0.05 significance level to test the claim that Statdisk generates the digits in a way that they are equally likely.

Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Questions 6–10 refer to the sample data in the following table, which describes the fate of the passengers and crew aboard the Titanic when it sank on April 15, 1912. Assume that the data are a sample from a large population and we want to use a 0.05 significance level to test the claim that surviving is independent of whether the person is a man, woman, boy, or girl.

Identify the null and alternative hypotheses corresponding to the stated claim.

Questions 6–10 refer to the sample data in the following table, which describes the fate of the passengers and crew aboard the Titanic when it sank on April 15, 1912. Assume that the data are a sample from a large population and we want to use a 0.05 significance level to test the claim that surviving is independent of whether the person is a man, woman, boy, or girl.

What distribution is used to test the stated claim (normal, t, F, chi-square, uniform)?

Questions 6–10 refer to the sample data in the following table, which describes the fate of the passengers and crew aboard the Titanic when it sank on April 15, 1912. Assume that the data are a sample from a large population and we want to use a 0.05 significance level to test the claim that surviving is independent of whether the person is a man, woman, boy, or girl.

Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Questions 6–10 refer to the sample data in the following table, which describes the fate of the passengers and crew aboard the Titanic when it sank on April 15, 1912. Assume that the data are a sample from a large population and we want to use a 0.05 significance level to test the claim that surviving is independent of whether the person is a man, woman, boy, or girl.

Find the number of degrees of freedom.

Testing Hypotheses About Regression Coefficients If the coefficient has a nonzero value, then it is helpful in predicting the value of the response variable. If it is not helpful in predicting the value of the response variable and can be eliminated from the regression equation. To test the claim that use the test statistic Critical values or P-values can be found using the t distribution with degrees of freedom, where k is the number of predictor variables and n is the number of observations in the sample. The standard error is often provided by software. For example, see the accompanying StatCrunch display for Example 1, which shows that (found in the column with the heading of “Std. Err.” and the row corresponding to the first predictor variable of height). Use the sample data in Data Set 1 “Body Data” and the StatCrunch display to test the claim that Also test the claim that What do the results imply about the regression equation?

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Cybersecurity The table below lists the frequency of leading digits of Internet traffic interarrival times for a computer, along with the percentages of each leading digit expected with Benford’s law.

a. Identify the general notation used for observed and expected values.

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