A university financial aid office polled a random sample of 467 male undergraduate students and 574 female undergraduate students. Each of the students was asked whether or not they were employed during the previous summer. 270 of the male students and 290 of the female students said that they had worked during the previous summer. Give a 90%confidence interval for the difference between the proportions of male and female students who were employed during the summer. Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval. Round your answer to three decimal places.                                           Step 2 of 3: Find the margin of error. Round your answer to six decimal places. Step 3 of 3: Construct the 90%confidence interval. Round your answers to three decimal places.

Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time,  μ , spent by customers at the supermarkets has been reported to be  35  minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that  μ  is less than  35  minutes. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be  31  minutes and the standard deviation of the times to be  15  minutes.   Based on this information, answer the questions below. What are the null hypothesis ( H0 ) and the alternative hypothesis ( H1 ) that should be used for the test? H0 :  μ  is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?313515 H1 :  μ  is ?less thanless than or equal togreater thangreater than or equal tonot…

Assume that the following samples are independent. In a random sample of 400 women, 47% favored health care reform. In a random sample of 300 men, 36% favored health care reform. Construct a 98% confidence interval for the difference between the population proportions p1 − p2 . Based on your interval, is there a significant difference between men and women’s opinions on health care reform? Explain. Calculator function:

A student found that in a random sample of 300 people in a town, 105 play sports. Based on this sample, construct a 90% confidence interval for the population proportion of all people in the town who play sports.Give your answers as decimals, rounded to three decimal places.