The entrance rate into a prestigious university's graduate program is 13%. a statistics student wants to know if the entrance rate of applicants from byu-idaho is greater than the typical entrance rate. he decides to conduct a hypothesis test of one proportion to determine whether the entrance rate of byu-idaho students into the graduate program is higher than 13%. he randomly selects 60 students who have applied and records whether or not each student was admitted. were the requirements for the hypothesis test met? explain.

Abottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company. the water bottling company’s specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. a random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 gallon a. construct a 99% confidence interval estimate for the popula-tion mean amount of water included in a 1-gallon bottle. b. on the basis of these results, do you think that the distributor has a right to complain to the water bottling company? why? c. must you assume that the population amount of water per bottle is normally distributed here? explain. d. construct a 95% confidence interval estimate. how does this change your answer to (b)?