According to the American College Review , average tuition at a 4-year private college is $15,858 with a standard deviation of $2,450. A particular parent, checking prices for a child about to go away...

According to the
American College Review, average tuition at a 4-year private college is $15,858 with a standard deviation of $2,450.  A particular parent, checking prices for a child about to go away to college, believes the average tuition is actually different than that and samples 40 colleges to test her theory.  The sample result shows average tuition to be $16,607.  Develop the hypothesis test and the ninety-five percent confidence interval needed to mathematically support this belief.  Is the parent right