Dr. Steve Brule is interested in the proportion of college students who like Cheesing. Let the proportion of college students who like Cheesing be p. If Dr. Steve Brule wanted to know if the proportion of college students who like cheesing differed from 35%, what are the null and alternative hypotheses

Arandom sample of n = 25 observations is taken from a n(µ, σ ) population. a 95% confidence interval for µ was calculated to be (42.16, 57.84). the researcher feels that this interval is too wide. you want to reduce the interval to a width at most 12 units. a) for a confidence level of 95%, calculate the smallest sample size needed. b) for a sample size fixed at n = 25, calculate the largest confidence level 100(1 − α)% needed.