An SRS of 350 high school seniors gained an average of =45 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation=26. Suppose we had an SRS of just 100 high school seniors. What would be the margin of error for 99% confidence? Give your answer to three decimalplaces.

2)Many young men in North America and Europe (but not in Asia) tend to think they need more muscle to be attractive. One study presented 200young American men with 100 images of men with various levels of muscle. Researchers measure level of muscle in kilograms per square meter of body surface area (kg/m2).Typical young men have about 20kg/m2. Each subject chose two images, one that represented his own level of body muscle and one that he thought represented "what women prefer." The mean gap between selfimage and "what women prefer" was2.35kg/m2.

Suppose that the "muscle gap" in the population of all young men has a Normal distribution with standard deviation 2.5kg/m2. Give a 90% confidence interval for the mean amount of muscle young men think they should add to be attractive to women. (They are wrong: women actually prefer a level close to that of typicalmen.)

Give your answers to four decimalplaces.

3)A class survey in a large class for firstyear college students asked, "About how many hours do you study during a typical week?" The mean response of the 463 students was =13.7hours. Suppose that we know that the study time follows a Normal distribution with standard deviation =7.4hours in the population of all firstyear students at this university. The99% confidence interval was found to be approximately 12.814 to 14.586hours.

There were actually 464 responses to the class survey. One student had claimed to study hours10,000hours per week (10,000 is more than the number of hours in a year). We know that student is joking, so we left out this value. If we did a calculation without looking at the data, we would get =35.2 hours for all 464 students. Now what is the 99%99% confidence interval for the population mean? (Continue to use =7.4.) Give your answers to three decimalplaces.