Suppose that a simple random sample of 60 college students is selected. At the college the students attend, the mean GPA is 3.1, with a standard deviation of 0.93.
(a) What shape would the sampling distribution of the mean GPA have? Does it depend on the population distribution?
(b) What would the mean of the sampling distribution be? What would the standard error be?
(c) What is the probability that the sample of students have a mean GPA below 3.0?
(d) Suppose that a new simple random sample of 100 students is selected. Is their mean GPA likely to be a better or worse estimator of the population GPA? Explain using the standard error of the sample mean.