Question

A golf association requires that golf balls have a diameter that is 1.68 inches. To determine if golf balls conform to the​ standard, a random sample of golf balls was selected. Their diameters are shown in the accompanying data table. Do the golf balls conform to the​ standards? Use the alphaαequals=0.01 level of significance.

Diameter_(in.)
1.683
1.686
1.684
1.685
1.676
1.677
1.685
1.682
1.681
1.686
1.673
1.674

First determine the appropriate hypotheses.

Now find the test statistic t 0 This can be found using technology or the formula​ below, where x overbarx is the sample​ mean, mu 0μ0 is the hypothesized​ mean, s is the sample standard​ deviation, n is the sample​ size, and the test statistic follows​ Student's t-distribution with n−1 degrees of freedom.

Find the​ P-value for this hypothesis test. Identify the​ P-value from your technology​ output, rounding to three decimal places.

Answer 1

The null and alternative hypothesis

Test statistic is

=0.73

degrees of freedom = n-1=12-1=11

P value =0.483

Note : This is a two tailed test ( as alternative hypothesis is ) , we find two tailed P value using excel

"=T.DIST.2T(M13,11)"

Since P value > 0.01 ( significance level)

we fail to reject H0

There is not sufficient evidence to conclude that diameter is different from 1.68 inches .

Calculation

	x	(x-)2
	1.683	0.000004
	1.686	0.000025
	1.684	0.000009
	1.685	0.000016
	1.676	0.000025
	1.677	0.000016
	1.685	0.000016
	1.682	0.000001
	1.681	0.000000
	1.686	0.000025
	1.673	0.000064
	1.674	0.000049
sum/ss	20.172	0.000250
	1.681
s2		0.000023
s		0.004767313