Please assist with these questions showing steps. Thank you.

1. The weights of a sample of 15 New York models had a sample mean of 107 lbs and a sample standard deviation of 10 lbs. Twelve Boston models had a sample mean of 112 lbs with a sample standard deviation of 8 lbs.Find the 90% confidence interval for the difference in weights between the two model populations.

1. The student government of a large college polled a random sample of 325 male students and found that 221 were in favor of a new grading system. At the same time, 120 out of a random sample of 220 female students were in favor of the new system. A counselor claimed the results would be the same. Test the claim at 5% significance level.

1. A reading test is given to an elementary school class that consist of 12 Anglo-American children and 10 Mexican-American children. The results of the test are - Anglo-American children:mean average of 74 with a S = 8;the Mexican-American children: mean average of 70 with a S = 10. Is the difference significant at a 5% significance level? Assume Ho states they are the same.

1. Hospital records show that of 500 men who were admitted for treatment, 60 were admitted because of high blood pressure. Of 500 women who were admitted for treatment, 50 were admitted for high blood pressure. Construct the 95% confidence interval estimate for the difference of the proportion of men and women that have high blood pressure.