A survey found that 18 out of 47 women voted for the proposition and 5 out of 55 men voted for the proposition. Find the absolute value of the test statistic when testing the claim that the proportion of women who voted for the proposition is greater than the proportion of men who voted for the proposition. (Round your answer to nearest hundredth. Hint: The correct test statistic is positive.)

A marketing survey involves product recognition in New York and California. Of 197 New Yorkers surveyed, 38 knew the product while 95 out of 299 Californians knew the product. At the 1.5% significance level, use the p-value method to test the claim that the recognition rates are the same in both states. Enter the test statistic. (Round your answer to nearest hundredth.)

Researchers conducted a study to determine whether magnets are effective in treating back pain. The results (higher values indicate larger reductions in pain levels) are shown in the table for the treatment (with magnets) group and the sham (or placebo) group. treatment sham sample size 19 22 mean 12 10 standard deviation 4 3 Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Use the critical value method and a 0.01 significance level to test the claim that the treatment mean measure of reduction in back pain is equal to the sham mean measure of reduction in back pain. (Hint: Consider statistictreatment-statisticsham.) Enter the smallest critical value. (Round your answer to nearest thousandth.)