Question

A researcher claims that the mean of the salaries of elementary school teachers is greater than the mean of the salaries of secondary school teachers in a large school district. The mean of the salaries of a random sample of 26 elementary school teachers is $49,099, and the sample standard deviation is $3,839.99. The mean of the salaries of a random sample of 24 secondary school teachers is $45,609. The sample standard deviation is $5,407. At α = 0.05, can it be concluded that the mean of the salaries of the elementary school teachers is greater than the mean of the salaries of the secondary school teachers? Use the P-value method.

Answer 1

Let , be the population mean of the salaries of the elementory school teachers and be the population mean of the salaries of the secondary school teachers.

The null and alternative hypothesis is ,

The test is one-tailed test.

Now , the degrees of freedom is ,

The test statistic is ,

The p-value is ,

p-value= ; The Excel function is , =TDIST(2.612,41,TRUE)

Decision : Here , p-value=0.0063<0.05

Therefore , reject Ho.

Conclusion : Hence , there is sufficient evidence to support the claim that the mean of the salaries of the elementary school teachers is greater than the mean of the salaries of the secondary school teachers.