The acceptance rate for a random sample of 15 medical schools in the United States was taken. The mean acceptance rate for this sample was 5.77 with a standard error of 0.56. Assume the distribution of acceptance rates is Normal.

a. Decide whether each of the following statements is worded correctly for the confidence interval. Fill in the blanks for the correctly worded one(s). Explain the error for the ones that are incorrectly worded.

i. We are 95% confident that the sample mean is between ___ and ___.

ii. We are 95% confident that the population mean is between ___ and ___.

iii. There is a 95% probability that the population mean is between ___ and ___.

b. Based on your confidence interval, would you believe the average acceptance rate for medical schools is 6.5? Explain.