Questions: A golf association requires that golf balls have a diameter that is 1 the standard, a random sample of golf balls was selected. Their d Do the golf balls conform to the standards? Use the alpha=0.01 level First determine the appropriate hypotheses. H0: μ=1.68 H1: μ=1.68 (Type integers or decimals. Do not round.) Find the test statistic. (Round to two decimal places as needed.)

Solution Steps

The sample mean \( \bar{x} \) is calculated as follows:

\[ \bar{x} = \frac{\sum_{i=1}^N x_i}{N} = \frac{16.79}{10} = 1.68 \]

The variance \( \sigma^2 \) is calculated using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n-1} = 0.0 \]

Thus, the standard deviation \( \sigma \) is:

\[ \sigma = \sqrt{0.0} = 0.01 \]

The standard error \( SE \) is given by:

\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{0.01}{\sqrt{10}} \approx 0.0032 \]

The test statistic \( t \) is calculated using the formula:

\[ t = \frac{\bar{x} - \mu_0}{SE} = \frac{1.68 - 1.68}{0.0032} = 0.0 \]

For a two-tailed test, the P-value is calculated as:

\[ P = 2 \times (1 - T(|z|)) = 1.0 \]

Since the P-value \( 1.0 \) is greater than the significance level \( \alpha = 0.01 \), we fail to reject the null hypothesis.

Final Answer