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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 [tex] \alpha = 0.10 [/tex], can you reject the personnel director's claim?

A. Z Test
B. T Test
C. 1 Prop Z Test
D. [tex] x^2 [/tex] test for [tex] \sigma [/tex]
E. 2-Sample Z Test
F. 2-Sample T Test
G. Dependent Sample T-Test
H. 2-Prop Z test
I. ANOVA Test

Answer :

Conduct 2-Sample T Test (unequal variances) to statistically assess difference in mean household income between Kauai Maui counties.


Determining the Appropriate Test:
To answer the question of whether the mean household income differs between Kauai and Maui counties, we need to compare the two samples. Here's how we can eliminate the irrelevant options:
a, c, d, g, h:

These tests are not suitable for comparing means between two independent groups (Kauai and Maui).
i: ANOVA is used for multiple groups, not just two.
Leaving us with b, e, and f.
b. T Test: While a T-Test is used for comparing means, it assumes equal variances (homoscedasticity). We don't have information about the population variances, so this might not be the best choice.
e. 2-Sample Z Test: This test applies when we have large samples (> 30) and know the population variances. We have moderate sample sizes but lack population variance information, making it a poor choice.
f. 2-Sample T Test: This test works for comparing means between independent groups with unequal variances (no homoscedasticity). It uses degrees of freedom based on the smaller sample size (Kauai = 18) for more robust results.
Therefore, the most appropriate test is:
f. 2-Sample T Test (unequal variances)

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