In a sample of 855 bartenders, 48% report hearing complaints from patrons about their jobs. If the margin of error for the proportion of bartenders hearing job complaints is 4.6 percentage points, what is the degree of confidence used?

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.