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Five-Step Hypothesis Test

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Past records suggest that the mean annual income, mu1, of teachers in state of Georgia is greater than or equal to the mean annual income, mu2, of teachers in Indiana. In a current study, a random sample of 20 teachers from Georgia and an independent random sample of 20 teachers from Indiana have been asked to report their mean annual income.The data obtained are as follows.

Annual income in dollars
Georgia 30964,36499,43508,40036,29752,36613,35317,42073,42721,37973,37954,
31990,42717,46182,35264,43142,43170,33550,38698,31504
Indiana 40452,39088,38551,35948,49637,40013,5215034665,41984,43107,37433,
42592,4689433281,45760,49092,40188,40973,33208,46104

The population standard deviation for mean annual income of teachers in Georgia and in Indiana are estimated as 6500 and 6600, 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 Georgia is greater than or equal to the mean annual income of teachers in Indiana? Perform a one-tailed test. Provide answers to the questions below.

Carry your intermediate computations to at least three decimal places and round your answers as specified below.

1. The null hypothesis Ho =

2. The alternative hypothesis H1 =

3. The type of test statistic(choose one) Z , t if so, provide degrees of freedom , chi
square if so, provide degrees of freedom , F if so provide dfn and dfd

4. The value of the test statistic(round to at least 3 decimal places)

5. The critical value at the 0.01 level of significance(round to at least 3 decimal places)

6. Can we reject the claim that the mean annual income of teachers from Georgia is greater than or equal to the mean annual income of teachers from Indiana? Yes or No

Please provide numerical answers where indicated. Thank you.

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Past records suggest that the mean annual income, mu1, of teachers in state of Georgia is greater than or equal to the mean annual income, mu2, of teachers in Indiana. In a current study, a random sample of 20 teachers from Georgia and an independent random sample of 20 teachers from Indiana have been asked to report their mean annual income. The data obtained are as follows.

Annual income in dollars
Georgia 30964,36499,43508,40036,29752,36613,35317,42073,42721,37973,37954, g31990,42717,46182,35264,43142,43170,33550,38698,31504
Indiana 40452,39088,38551,35948,49637,40013,5215034665,41984,43107,37433,
i42592,46894,33281,45760,49092,40188,40973,33208,46104

The population standard deviation for mean annual income of teachers in Georgia and in Indiana are estimated as 6500 and 6600, respectively. It is also known that both populations are approximately normally distributed. At the 0.01 level of ...

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