Is there any difference in the variability in golf scores for players on a women's professional golf tour and players on a men's professional golf tour? A sample of 20 tournament scores from events in a tour for women showed a standard deviation of 2.4638 strokes, and a sample of 30 tournament scores from events in a tour for men showed a standard deviation of 2.2121. Conduct a hypothesis test for equal population variances to determine if there is any statistically significant difference in the variability of golf scores for male and fernale professional golfers. Use a = 0.10.

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Is there any difference in the variability in golf scores for players on a women's professional golf tour and players on a men's professional golf tour? A sample of 20 tournament scores from events in a tour for women showed a standard deviation of 2.4638 strokes, and a sample of 30 tournament scores from events in a tour for men showed a standard deviation of 2.2121. Conduct a hypothesis test for equal population variances to determine if there is any statistically significant difference in the variability of golf scores for male and female professional golfers. Use \(\alpha = 0.10\).

State the null and alternative hypotheses.

- \(H_0: \sigma^2_1 < \sigma^2_2\)
- \(H_a: \sigma^2_1 \geq \sigma^2_2\)

- \(H_0: \sigma^2_1 = \sigma^2_2\)
- \(H_a: \sigma^2_1 \neq \sigma^2_2\)

- \(H_0: \sigma^2_1 > \sigma^2_2\)
- \(H_a: \sigma^2_1 \leq \sigma^2_2\)

- \(H_0: \sigma^2_1 = \sigma^2_2\)
- \(H_a: \sigma^2_1 > \sigma^2_2\)

Find the value of the test statistic. (Round your answer to two decimal places.)

\[
\text{Test statistic} = \_\_\_\_\_
\]

Find the \(p\)-value. (Round your answer to four decimal places.)

\(p\)-value = \_\_\_\_

State your conclusion.

- Reject \(H_0\). We can conclude that there is a difference in the variability of golf scores for male and female professional golfers.

- Do not reject \(H_0\). We cannot conclude that there is a difference in the variability of golf scores for male and female professional golfers.
Transcribed Image Text:Is there any difference in the variability in golf scores for players on a women's professional golf tour and players on a men's professional golf tour? A sample of 20 tournament scores from events in a tour for women showed a standard deviation of 2.4638 strokes, and a sample of 30 tournament scores from events in a tour for men showed a standard deviation of 2.2121. Conduct a hypothesis test for equal population variances to determine if there is any statistically significant difference in the variability of golf scores for male and female professional golfers. Use \(\alpha = 0.10\). State the null and alternative hypotheses. - \(H_0: \sigma^2_1 < \sigma^2_2\) - \(H_a: \sigma^2_1 \geq \sigma^2_2\) - \(H_0: \sigma^2_1 = \sigma^2_2\) - \(H_a: \sigma^2_1 \neq \sigma^2_2\) - \(H_0: \sigma^2_1 > \sigma^2_2\) - \(H_a: \sigma^2_1 \leq \sigma^2_2\) - \(H_0: \sigma^2_1 = \sigma^2_2\) - \(H_a: \sigma^2_1 > \sigma^2_2\) Find the value of the test statistic. (Round your answer to two decimal places.) \[ \text{Test statistic} = \_\_\_\_\_ \] Find the \(p\)-value. (Round your answer to four decimal places.) \(p\)-value = \_\_\_\_ State your conclusion. - Reject \(H_0\). We can conclude that there is a difference in the variability of golf scores for male and female professional golfers. - Do not reject \(H_0\). We cannot conclude that there is a difference in the variability of golf scores for male and female professional golfers.
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