Question

A golf balls manufacturer requires that the weights of its golf balls have a standard deviation that is less or equal 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 weighs 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)

H0: $\sigma$ <= 0.08

Ha: $\sigma$ > 0.08

b)

Test statistics

$\chi^{2}$ = (n - 1) * S2 / $\sigma$ 2

= ( 50 - 1) * 0.08062 / 0.082

= 49.74

C)

Critical value at 0.01 significance level with 49 df = 74.92

Rejection rule = Reject H0 if $\chi^{2}$ > 74.92

D)

Decision = Since test statistics falls in non-rejection region , fail to reject H0.

E)

We do not have sufficient evidence to support the claim that the standard deviation of the weighs of the

golf balls is more than 0.08 ounces.