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

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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

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