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# Hypothesis Testing - Annual Income in Pennsylvania

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Past records suggest that the mean annual income, u1, of teachers in state of Pennsylvania is less than or equal to the mean annual income, u2, of teachers in Illinois. In a current study, a random sample of 15 teachers from Pennsylvania and an independent random sample of 15 teachers from Illinois have been asked to report their mean annual income. The data obtained are as follows:

Penn. Ill.
45192 43638
51542 50081
51054 40936
49091 52578
47925 37369
49515 42721
49140 48893
54768 42009
45279 39274
43012 54691
40893 38305
48707 30938
55258 47207
49583 41240
39795 34222

The population standard deviation for mean annual income of teachers in Pennsylvania and in Illinois are estimated as 6400 and 6100, 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 Pennsylvania is less than or equal to the mean annual income of teachers in Illinois? 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 of the mean annual income of teachers from Pennsylvania is less than or equal to the mean annual income of teachers from Illinois? Yes or no