Question

In Exercise $10.83$, you conducted a nonpooled $t$-test to decide whether the mean number of acute postoperative days spent in the hospital is smaller 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. Which test do you think is more appropriate, the pooled or nonpooled $t$-test? Explain your answer.

Short answer

(a) Since, $P\le \alpha ,(0.012\le 0.05)$, so, the hypothesis is rejected for $5\%$level.

(b)A pooled t-test is used to reject the null hypothesis rather than a non pooled t-test.

(c)Because the standard deviations of two variables are not comparable, the non-pooled t-test is suitable.

Step-by-step solution

Part (a) Step 1: Given information

Given in the question that , In Exercise 10.83, you conducted a nonpooled $t$-test to decide whether the mean number of acute postoperative days spent in the hospital is smaller with the dynamic system than with the static system. Use the technology of your choice to perform the following tasks.

we need to repeat that hypothesis test using a pooled $t$-test.

Part (a) Step 2: Explanation

The output is,

The test statistic has a value of $2.45$.

$0.012$is the P-value.

The hypothesis is rejected for the $5\%$level using the P-value technique, because $P\le \alpha ,,(0.012\le 0.05)$.

Part (b) Step 1: Given information

Given in the question that, In Exercise 10.83, you conducted a nonpooled $t-$test to decide whether the mean number of acute postoperative days spent in the hospital is smaller with the dynamic system than with the static system. Use the technology of your choice to perform the following tasks.

we need to compare results from the pooled and nonpooled $t$-tests.

Part (b) Step 2: Explanation

A pooled $t$-test is used to reject the null hypothesis rather than a non pooled $t$-test.

Part (c) Step 1: Given information

Given in the question that,

In Exercise 10.83, you conducted a nonpooled$t$-test to decide whether the mean number of acute postoperative days spent in the hospital is smaller with the dynamic system than with the static system. Use the technology of your choice to perform the following tasks.

we need to find the more appropriate test.

Part (c) Step 2: Explanation

Because the standard deviations of two variables are not comparable, the non-pooled $t$-test is suitable. Furthermore, the sample sizes are variable.