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Hypothesis Test

Problem:

Past records suggest that the mean annual income, mu1, of teachers in state of pennsylvania is less than or equal to the mean annual income, mu2, 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:

Annual income in dollars:

Pennsylvania: 48328, 50306, 60240, 51475, 45907, 53775, 41891, 54579, 56691, 49082, 50803, 54491, 46189, 45232, 41828
Illinois: 43658, 52307, 39589, 45643, 44440, 39322, 32237, 50639, 39983, 37811, 36605, 44425, 40391, 56138, 48695

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 0.01 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.

Question:

H0:_____
H1:_____
Type of test statistic: (Z, t, F, or Chi squared)
Value of test statistic:______
The p-value:_______
Can we reject the claim that the mean annual income of teachers from Pennsylvania is less than or equal to the mean annual income of teachers from Illinois?

Solution Preview

Problem:

Past records suggest that the mean annual income, mu1, of teachers in state of Pennsylvania is less than or equal to the mean annual income, mu2, 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:

Annual income in dollars:

Pennsylvania: 48328, 50306, 60240, 51475, 45907, 53775, 41891, 54579, 56691, 49082, 50803, 54491, 46189, 45232, 41828

Illinois: 43658, 52307, 39589, 45643, 44440, 39322, 32237, 50639, 39983, 37811, 36605, 44425, 40391, 56138, 48695

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 0.01 level of ...

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