A random sample of 10 colleges from Kiplinger’s 100 Best Values in Public Education was taken. The mean rate of graduation within four years was 43.5% with a margin of error of 6.0%. The distribution of graduation rates is Normal.
a. Decide whether each of the following statements is worded correctly for the confidence interval, and fill in the blanks for the correctly worded one(s).
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. Can we reject a population mean percentage of 50% on the basis of these numbers? Explain.