I need an explanation for this Statistics question to help me study.
1. Sample data shows that 20 out of 48 students with cell phones passed the course and 1 out of 95 students without cell phones passed the course. Find the absolute value of the test statistic when testing the claim that the proportion of students with cell phones passed the course is not more than the proportion of students without cell phones passed the course. (Round your answer to nearest hundredth. Hint: The correct test statistic is positive.)
2. A marketing survey involves product recognition in New York and California. Of 32 New Yorkers surveyed, 200 knew the product while 93 out of 297 Californians knew the product. At the 2.5% significance level, use the critical value method to test the claim that the recognition rates are different in the states.
Enter the test statistic. (Round your answer to nearest hundredth.)
3. 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 0.05 significance level to test the claim that the treatment mean measure of reduction in back pain is greater than the sham mean measure of reduction in back pain. (Hint: Consider statistictreatment-statisticsham.)
Enter the test statistic. (Round your answer to nearest thousandth.)