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Chapter 8: Q4CQQ (page 356)
P-Value Find the P-value in a test of the claim that the mean annual income of a CIA agent is greater than $81,623 (based on data from payscale.com) given that the test statistic is t = 1.304 for a sample of 40 CIA agents.
The p-value is equal to 0.10.
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Final Conclusions. In Exercises 25–28, use a significance level of = 0.05 and use the given information for the following:
a. State a conclusion about the null hypothesis. (Reject or fail to reject .)
b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.
Original claim: More than 58% of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.3257.
Testing Claims About Proportions. In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.
Overtime Rule in Football Before the overtime rule in the National Football League was changed in 2011, among 460 overtime games, 252 were won by the team that won the coin toss at the beginning of overtime. Using a 0.05 significance level, test the claim that the coin toss is fair in the sense that neither team has an advantage by winning it. Does the coin toss appear to be fair?
Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.
Heights of Supermodels Listed below are the heights (cm) for the simple random sample of female supermodels Lima, Bundchen, Ambrosio, Ebanks, Iman, Rubik, Kurkova, Kerr,Kroes, Swanepoel, Prinsloo, Hosk, Kloss, Robinson, Heatherton, and Refaeli. Use a 0.01 significance level to test the claim that supermodels have heights with a mean that is greater than the mean height of 162 cm for women in the general population. Given that there are only 16 heights represented, can we really conclude that supermodels are taller than the typical woman?
178 177 176 174 175 178 175 178 178 177 180 176 180 178 180 176
Final Conclusions. In Exercises 25–28, use a significance level of = 0.05 and use the given information for the following:
a. State a conclusion about the null hypothesis. (Reject or fail to reject .)
b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.
Original claim: Fewer than 90% of adults have a cell phone. The hypothesis test results in a P-value of 0.0003.
Technology. In Exercises 9–12, test the given claim by using the display provided from technology. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.
Old Faithful Data Set 23 “Old Faithful” in Appendix B includes data from 250 random eruptions of the Old Faithful geyser. The National Park Service makes predictions of times to the next eruption, and the data set includes the errors (minutes) in those predictions. The accompanying Statdisk display results from using the prediction errors (minutes) to test the claim that the mean prediction error is equal to zero. Comment on the accuracy of the predictions.
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