In 2019, another study on college student performance was conducted for students from school A.

In 2019, another study on college student performance was conducted for students from School A. Assume that the GPAs were normally distributed. A random sample of 10 students was found to have the following GPAs: 3.45, 3.3, 3.27, 3.27, 2.81, 2.8, 2.65, 2.89, 3.36, 2.53. Question 8: Suppose that the standard deviation of the GPAs was the same as in 2017, and that, in 2017, the margin of error at a confidence level of 95% for the mean GPA for samples of size 25 is 0. 1764. Find an estimate for the mean GPA (in 2019) with 95% confidence. Question 9: The assumption made in Question 8 was unrealistic. Find an estimate for the mean GPA (in 2019) with 95% confidence based on the sample provided Question 10: Find an estimate for the variance of the GPAs (in 2019) with 95% confidence based on the sample provided. Question 11: Suppose that in a random sample of 400 students who earned a GPA of 3.5 or above, 47% were males. Find an estimate for the percentage of females among all students who earned a GPA of 3.5 or above with 95% confidence. In 2021, a similar study on college student performance is to be conducted for students from School A. The goal is to estimate the mean GPA. Assume that the GPAs are normally distributed. Question 12: Suppose that the standard deviation of the GPAs is the same as in 2017, and that, in 2017, the margin of error at a confidence level of 95% for the mean GPA for samples of size 25 is 0.1764. Find the minimum size of the sample if the margin of error at a confidence level of 98% for the mean GPA (in 2021) does not exceed 0.1