Question

A survey indicates that the mean annual wages for forensic science technicians working for local and state governments are $60,680 and $59,430, respectively. The survey includes a randomly selected sample of size 100 from each government branch. Assume that the population standard deviations are $6200 (local) and $5575 (state). The two samples are independent. At alpha = 0.10, is there enough evidence to conclude that there is a difference in the mean annual wages?

Answer 1

The standard error here is computed as:

The test statistic here is computed as:

For n₁ + n₂ - 2 = 198 degrees of freedom, we have from the t distribution tables here:

p = 2P(t₁₉₈ > 1.5) = 2*0.0677 = 0.1354

As the p-value here is 0.1354 > 0.1 which is the level of significance, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we have insufficient evidence here that there is a difference in two means here.