Line segment EF is shown on a coordinate grid: The line segment is rotated 180 degrees counterclockwise about the origin to form E′F′. Which statement describes E′F′? (4 points)

a
E′F′ is perpendicular to EF.

b
E′F′ and EF are equal in length.

c
E′F′ is half the length of EF.

d
E′F′ is greater than twice the length of EF.

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.