(1) When testing gas pumps for accuracy, fuel-quality enforcement specialists tested pumps and found that 1272 of them were not pumping accurately (within 3.3 oz when 5 gal is pumped), and 5690 pumps were accurate. Use a 0.01 significance level to test the claim of an industry representative that less than 20% of the pumps are inaccurate. Use the P-value method and use the normal distribution as an approximation to the binomial distribution. The test statistic is z and P-value?
(2) A survey of 61,649 people included several questions about office relationships. Of the respondents, 27.3% reported that bosses scream at employees. Use a 0.05 significance level to test the claim that more than 1/4 of people say that bosses scream at employees. How is the conclusion affected after learning that the survey is an online survey in which Internet users chose whether to respond? Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution .The test statistic is z and P-value
(3) Trials in an experiment with a polygraph include 97 results that include 23 cases of wrong results and 74 cases of correct results. Use a 0.01 significance level to test the claim that such polygraph results are correct less than 80% of the time. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution. The test statistic is z and P-value