Decide whether or not each equation represents a proportional relationship. Answer each question with yes or no. Volume measured in cups (c) vs. the same volume measured in ounces (z): c=18z
Area of a square (A) vs. the side length of the square (s): A = s2
Perimeter of an equilateral triangle (P) vs. the side length of the triangle (s): 3s=P
Length (L) vs. width (w) for a rectangle whose area is 60 square units: L=60w

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.