In one weekend, 1,200 people attend a play at the theater downtown. A survey of 100 people who attended found that 45 gave the play at least 4 stars out of 5. Use the indicated method to estimate how many people in all would give the play at least 4 stars.

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.