Question

A manufacturing process produces Ping-Pong balls with diameters that have a normal distribution with known population standard deviation of .04 centimeters. Ping-Pong balls with diameters that are too small or too large are considered defective. The manufacturing company claims all their Ping-Pong balls have a diameter of exactly = 0.50 centimeters. Perform a hypothesis test at the 5% level of significance to check if the claim is true. Assume that a random sample of 25 gave a mean diameter of 0.51 centimeters. Perform a hypothesis test and state your decision using critical value approach.

Answer 1

bolun- Given population standard deviol'on = 0 = 0.04 centimeters Aim - The manufacturing company clarme that all their ping- pong balls have a diameter of exactly 0.50 centimelers. Hypothesis Ho! U = 0.50 Cclaim) He : H0.50 (two sided hypothesis) Random sample of m=25 ; mean = K = 0.51 : Here population standard devialton is known so we use z-test Test Stalistic: X-u olun Z = 0.51-0.50 0.041525 1. Z - 1.25 critical Value / Rejection area : 591. Significance level =) 0=0.05 :: Critical value = Zorg = 1.96 012-0.025 (two sided) critical region 0.025 critical region 0.025 Tu -3-2-1 -1.96 0 3 1 1.2 1.96 Decision : bince Iz1 < Zain we Zailed to reject Mo at 5% devel 0% significance.so accept Ho. Conclusion : There is significant evidence to accept companies Claim that on thely Ping-Pong bolls have diometer of exactly 0.50 centimeters.