The transitive property of equality states that A. if a =b, then b =a
B. if a =b, then ac = bc
C. if a =b and b=c, then a =c
D. if a = b and c= c, then a + b =b+c

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.