Answer:
We conclude that the standard deviation of the diameter of a golf ball is less than 0.005 inch.
Step-by-step explanation:
We are given that a professional golfing association requires that the standard deviation of the diameter of a golf ball be less than 0.005 inch.
Assume that the population is normally distributed: 1.678, 1.681, 1.676, 1.684, 1.676, 1.679, 1.681, 1.681, 1.677, 1.676, 1.681, 1.683.
Let = <u><em>population standard deviation of the diameter of a golf ball.</em></u>
SO, Null Hypothesis, :
0.005 inch {means that the standard deviation of the diameter of a golf ball is more than or equal to 0.005 inch}
Alternate Hypothesis, :
< 0.005 inch {means that the standard deviation of the diameter of a golf ball is less than 0.005 inch}
The test statistics that would be used here <u>One-sample Chi-square test statistics</u>;
T.S. = ~
where, s = sample standard deviation = = 0.00281 inch
n = sample size = 12
So, <u><em>the test statistics</em></u> = ~
= 3.47
The value of chi-square test statistics is 3.47.
Also, the P-value of test statistics is given by the following formula;
P-value = P( < 3.47) = 0.0182
Since, the P-value of the test statistics is less than the level of significance as 0.0182 < 0.05, so we reject our null hypothesis.
<u>Now, at 0.05 significance level the chi-square table gives critical value of 4.575 at 11 degree of freedom for left-tailed test.</u>
Since our test statistic is less than the critical value of chi-square as 3.47 < 4.575, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u><em>we reject our null hypothesis</em></u>.
Therefore, we conclude that the standard deviation of the diameter of a golf ball is less than 0.005 inch.
