# One-Tailed Tests for Population Standard Deviation of Mean Income of Teachers

Past records suggest that the mean annual income, u1, of teachers in state of Utah is greater than or equal to the mean annual income, u2, of teachers in Oregon. In a current study, a random sample of 10 teachers from Utah and an independent random sample of 10 teachers from Oregon have been asked to report their mean annual income. The data obtained are as follows.

Utah ----Oregon

27060---41176

32575---43541

32664---31579

38068---35106

32384---27719

34132---37008

32925---30419

40826---41692

29920---37791

44864---30548

The population standard deviation for mean annual income of teachers in Utah and in Oregon are estimated as 6400 and 6500, respectively. It is also known that both populations are approximately normally distributed. At the 0.05 level of significance, is there sufficient evidence to reject the claim that the mean annual income of teachers in state of Utah is greater than or equal to the mean annual income of teachers in Oregon? Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table

Answer the following:

Null hypothesis:

Alternative hypothesis:

Type of test statistic:

Value of the test statistic rounded to at least 3 decimal places:

the p value rounded to at least 3 decimal places:

Can we reject the claim that the mean annual income of teachers from Utah is greater than or equal to the mean annual income of teachers from Oregon?

yes or no

https://brainmass.com/statistics/hypothesis-testing/one-tailed-tests-for-population-standard-deviation-of-mean-income-of-teachers-69869

#### Solution Summary

The solution attaches a .doc file giving the null/alternative hypotheses, value of test statistic, p value and conclusion for this question on mean annual income of teachers in Utah.