Which test should be conducted to answer the following problem?

A personnel director in Hawaii claims that the mean household income is the same in Kauai County and Maui County. In Kauai County, a sample of 18 residents has a mean household income of 56,900 and a standard deviation of 12,100. In Maui County, a sample of 20 residents has a mean household income of 57,800 and a standard deviation of 8,000. At alpha equals 0.10, can you reject the personnel director's claim?

1. Z test
2. T test
3. 1-prop Z test
4. Chi-squared test for sigma
5. 2-sample Z test
6. 2-sample T test
7. Dependent sample T-test
8. 2-prop Z test
9. ANOVA test

The appropriate test to answer this problem is the 2-sample T test. We compare the mean household incomes using the provided sample means, standard deviations, and sample sizes. Therefore correct option is (6)

Explanation:

The appropriate test to answer this problem is the 2-sample T test.

To conduct the test, we compare the mean household incomes of Kauai County and Maui County. The null hypothesis is that the mean household incomes are the same, while the alternative hypothesis is that they are different.

Using the provided sample means, standard deviations, and sample sizes, we calculate the test statistic and compare it to the critical value at a significance level of 0.10. If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the mean household incomes are different. If the test statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a difference in mean household incomes.

In this case, we compare the test statistic with the critical value for an alpha level of 0.10. If the test statistic is greater than the critical value, we reject the personnel director's claim. If the test statistic is less than the critical value, we fail to reject the claim.