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 randorn 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 $\alpha=0.01$ level of significance.
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Find the test statistic.
0.76
(Round to two decimal places as needed)
Find the $\mathrm{P}$-value.
0.461
(Round to three decimal places as needed)
What can be concluded from the hypothesis test?
A. Reject $\mathrm{H}_{0}$. There is sufficient evidence to conclude that the golf balls do not conform to the association's standards at the $\alpha=0.01$ level of significance
B. Do not reject $\mathrm{H}_{0}$. There is not sufficient evidence to conclude that the golf balls do not conform to the association's standards at the $\alpha=0.01$ level of significance.
C. Reject $\mathrm{H}_{0}$. There is not sufficient evidence to conclude that the golf balls do not conform to the association's standards at the $\alpha=0.01$ level of significance:
D. Do not reject $\mathrm{H}_{0}$. There is sufficient evidence to conclude that the golf balls do not conform to the association's standards at the $\alpha=0.01$ level of significance.
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Final Answer: \(\boxed{\text{B. Do not reject } H_{0}. \text{There is not sufficient evidence to conclude that the golf balls do not conform to the association's standards at the } \alpha=0.01 \text{ level of significance.}}\)
Step 1 ：The question is asking us to determine if the golf balls conform to the standard diameter of 1.68 inches. We are given a test statistic and a P-value. The test statistic is a measure of how much the sample data deviate from what is expected under the null hypothesis, which in this case is that the golf balls conform to the standard. The P-value is the probability of obtaining the observed data (or data more extreme) if the null hypothesis is true.
Step 2 ：We are asked to make a decision based on a significance level of 0.01. If the P-value is less than the significance level, we reject the null hypothesis. If the P-value is greater than the significance level, we do not reject the null hypothesis.
Step 3 ：In this case, the P-value is 0.461, which is greater than the significance level of 0.01. Therefore, we do not reject the null hypothesis. This means that there is not sufficient evidence to conclude that the golf balls do not conform to the association's standards at the 0.01 level of significance.
Step 4 ：Final Answer: \(\boxed{\text{B. Do not reject } H_{0}. \text{There is not sufficient evidence to conclude that the golf balls do not conform to the association's standards at the } \alpha=0.01 \text{ level of significance.}}\)
