Question

In Example \(10.6\) on pages \(420-422\), we conducted a nonpooled \(t-\)test, at the \(5%\) significance level, to decide whether the mean operative time is less with the dynamic system than with the static system. Use the technology of your choice to perform the following tasks.

a. Using a pooled \(t-\)test, repeat that hypothesis test.

b. Compare your results from the pooled and nonpooled \(t-\)tests.

c. Repeat both tests, using a \(1%\) significance level, and compare your results.

d. Which test do you think is more appropriate that pooled or nonpooled \(t-\)test? Explain your answer.

Short answer

Part a. \(P\leq \alpha (0.029\leq 0.05)\) so the hypothesis is rejected for \(5%\) level.

Part b. Comparing the result for both tests, the hypothesis is rejected. It means the mean operative time is less than the dynamic system than with the statistic system.

Part c. \(P\leq \alpha (0.008\leq 0.01)\) so, the hypothesis is rejected for \(1%\) level.

Part d. The non pooled \(t-\)test is appropriate because, the standard deviation for two variable are not equal. More ever, two sample size are also different.

Step-by-step solution

Part a. Step 1. Explanation

The output is shown below

The value of tests statistic is \(-2.02\).

The \(P-\)value is \(0.029\).

By \(P-\)value approach,

Since, \(P\leq \alpha (0.029\leq 0.05)\) so the hypothesis is rejected for \(5%\) level.

Part b. Step 1. Explanation

Comparing the result for both tests, the hypothesis is rejected. It means the mean operative time is less than the dynamic system than with the statistic system.

Part c. Step 1. Explanation

The output is shown below,

The value of tests statistic is \(-2.68\).

The P-value is \(0.008\).

By \(P-\)value approach,

Since, \(P\leq \alpha (0.008\leq 0.01)\) so, the hypothesis is rejected for \(1%\) level.

Part d. Step 1. Explanation

The non pooled \(t-\)test is appropriate because, the standard deviation for two variable are not equal. More ever, two sample size are also different.