Question

3. A personnel director from Indiana claims that the mean household income is greater in Monroe County than it is in Owen County. In Monroe County, a sample of 16 residents has a mean household income of $58,800 and a sample standard deviation of $8,800. In Owen County, a sample of 25 residents has a mean household income of $54,000 and a standard deviation of $5,100. At α = 0.05, can you support the personnel director’s claim? Assume the population variances are not equal.

Answer 1

The standard error for the test is first computed here as:

Now the test statistic here is computed as:

For n₁ + n₂ - 2 = 16 + 25 - 2 = 39 degrees of freedom, we get the p-value here as:

p = P( t₃₉ > 1.9794) = 0.0274

As the p-value here is 0.0274 < 0.05 which is the level of significance, therefore the test is significant and we can reject the null hypothesis here and conclude that we have sufficient evidence that the mean household income is greater in Monroe County than it is in Owen County.