The Connecticut Board of Education is concerned that first year male elementary

Question

The Connecticut Board of Education is concerned that first year male elementary school teachers are receiving lower salaries than their female counterparts. Two independent random samples have been selected: 720 observations from population 1 (male elementary school teachers) and 710 from population 2 (female elementary school teachers). The sample means obtained are X1(bar)=$35 k and X2(bar)=$36 k. It is known from previous studies that the population variances are 5.6 and 4.0 respectively. Using a level of significance of .10, is there evidence that the first year male elementary school teachers are receiving lower salaries? Fully explain your answer.

Explanation / Answer

Let the null hypothesis be that the mean for the males is greater than or equal to that of the females. The alternative is that the mean for the males is less. Because the population deviations are known, we can use the 2-sample z-test. The test statistic is The p-value for this 0.00005, which is signficant at the 10% level certainly!

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