Question

For this problem, solve the problems by answering a) state the claim using a sentence, b) Ho H1 and place the claim with either one of the two, c) Test statistic, show and label the formula you use, d) find critical value(s), and reject Ho or fail to reject Ho. You may use p-value. e) Write a formal conclusion and final statement (Please show all work and label answer a,b,c,d,e)

A golf balls manufacturer requires that the weights of its gold balls have a standard deviation that is less or equal to 0.08 ounces. One of the quality control inspectors says that the machines need to be recalibrated because he believes (claims) the standard deviation of the weights of the golf balls is more than 0.08 ounces. To test the machines, he selects a random sample of 50 golf balls off the assembly line and finds that they have a mean weight of 1.56 ounces and a standard deviation of 0.0806 ounces. At the 0.01 level of significance, test the inspector's claim.

a)

b)

c)

d)

e)

Answer 1

a)

cliam is the standard deviation of the weights of the golf balls is more than 0.08 ounces.

b)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 0.08
Alternative Hypothesis, Ha: σ > 0.08

c)

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (50 - 1)*0.0806^2/0.08^2
Χ^2 = 49.738

d)

This is right tailed test, for α = 0.01 and df = 49
Critical value of Χ^2 is 74.919
Hence reject H0 if Χ^2 < 74.919

fail to reject null hypothesis.

P-value Approach
P-value = 0.4437

As P-value >= 0.01, fail to reject null hypothesis.

e)

There is not sufficient evidence to conclude that the standard deviation of the weights of the golf balls is more than 0.08 ounces.