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Chapter 8: Q. 9.53 (page 370)
Which provides stronger evidence against the null hypothesis, a P-value of or a P-value of ? Explain your answer.
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Type I and Type II Errors. In Exercises 29鈥�32, provide statements that identify the type I error and the type II error that correspond to the given claim. (Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.).
The proportion of people with blue eyes is equal to 0.35.
Video Games: Checking Requirements Twelve different video games showing alcohol use were observed. The duration times of alcohol use were recorded, with the times (seconds) listed below (based on data from 鈥渃ontent and rating of Teen-Rated Video Games,鈥� by Haninger and Thompson, journal of the American Medical Association, Vol.291, No.7). What requirements must be satisfied to test the claim that the sample is from a population with a mean greater than 90 sec? Are the requirements all satisfied?
84 14 583 50 0 57 207 43 178 0 2 57
Testing Claims About Proportions. In Exercises 9鈥�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.
Store Checkout-Scanner Accuracy In a study of store checkout-scanners, 1234 items were checked for pricing accuracy; 20 checked items were found to be overcharges, and 1214 checked items were not overcharges (based on data from 鈥淯PC Scanner Pricing Systems: Are They Accurate?鈥� by Goodstein, Journal of Marketing, Vol. 58). Use a 0.05 significance level to test the claim that with scanners, 1% of sales are overcharges. (Before scanners were used, the overcharge rate was estimated to be about 1%.) Based on these results, do scanners appear to help consumers avoid overcharges?
Testing Claims About Proportions. In Exercises 9鈥�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.
Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Use a 0.01 significance level to test Mendel鈥檚 claim that under the same circumstances, 25% of offspring peas will be yellow. What can we conclude about Mendel鈥檚 claim?
Testing Hypotheses. In Exercises 13鈥�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.
Cans of Coke Data Set 26 鈥淐ola Weights and Volumes鈥� in Appendix B includes volumes (ounces) of a sample of cans of regular Coke. The summary statistics are n = 36, x = 12.19 oz, s = 0.11 oz. Use a 0.05 significance level to test the claim that cans of Coke have a mean volume of 12.00 ounces. Does it appear that consumers are being cheated?
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