Questions: Question 2 When deciding whether to use a pooled or non-pooled T procedure for testing a hypothesis about two population means, one has to check whether the populations variances can be assumed to be equal or not. However, it can't be done just by looking at the sample variances. Although the sample variances may not appear to be exactly the same it can be due to the sampling error. We want to statistically check the claim whether the variances are the same or not. To check this claim, the two-tail F-test for two variances was setup and the p-value was calculated to be 0.007. Interpret the results using the significance level of 1% and decide whether to use a pooled or non-pooled T procedure to test a claim about the population means. Under 1% significance level, there is Select an answer 0 to suggest that the two populations have different variances, therefore, to test a claim about the population means we would use the T Select an answer 0 procedure.

Question 2

When deciding whether to use a pooled or non-pooled T procedure for testing a hypothesis about two population means, one has to check whether the populations variances can be assumed to be equal or not. However, it can't be done just by looking at the sample variances. Although the sample variances may not appear to be exactly the same it can be due to the sampling error. We want to statistically check the claim whether the variances are the same or not. To check this claim, the two-tail F-test for two variances was setup and the p-value was calculated to be 0.007. Interpret the results using the significance level of 1% and decide whether to use a pooled or non-pooled T procedure to test a claim about the population means. Under 1% significance level, there is Select an answer 0 to suggest that the two populations have different variances, therefore, to test a claim about the population means we would use the T Select an answer 0 procedure.

Transcript text: Question 2 When deciding whether to use a pooled or non-pooled $T$ procedure for testing a hypothesis about two population means, one has to check whether the populations variances can be assumed to be equal or not. However, it can't be done just by looking at the sample variances. Although the sample variances may not appear to be exactly the same it can be due to the sampling error. We want to statistically check the claim whether the variances are the same or not. To check this claim, the two-tail F-test for two variances was setup and the p-value was calculated to be 0.007 . Interpret the results using the significance level of $1 \%$ and decide whether to use a pooled or non-pooled T procedưre to test a claim about the population means. Under $1 \%$ significance level, there is Select an answer 0 to suggest that the two populations have different variances, therefore to test a claim about the population means we would use the $T$ Select an answer 0 procedure.

Solution

Solution Steps

Step 1: Hypothesis Testing for Variances

To determine whether to use a pooled or non-pooled $ T $ procedure for testing a hypothesis about two population means, we first conduct an F-test for the variances. The null hypothesis $ H_0 $ states that the variances of the two populations are equal, while the alternative hypothesis $ H_a $ states that the variances are not equal.

Given the p-value from the F-test is $ p = 0.007 $ and the significance level is $ \alpha = 0.01 $, we compare the p-value to the significance level.

Step 2: Decision Rule

We apply the decision rule:

If $ p < \alpha $, we reject $ H_0 $.
If $ p \geq \alpha $, we fail to reject $ H_0 $.

In this case: \[ 0.007 < 0.01 \] Thus, we reject the null hypothesis $ H_0 $.

Step 3: Conclusion on Variances

Since we have sufficient evidence to suggest that the two populations have different variances, we conclude that the variances are not equal.

Step 4: Choice of T Procedure

Given that the variances are significantly different, we will use the non-pooled $ T $ procedure (Welch's t-test) to test a claim about the population means.