Question

Past records suggest that the mean annual income, μ 1, of teachers in state of New York is less than or equal to the mean annual income, μ of teachers in Illinois. In a current study, a random sample of 10 teachers from New York and an independent random sample of 10 teachers from Illinois have been asked to report their mean annual income. The data obtained are as follows: Annual income in dollars New York 38021, 49809, 38147, 43028, 43781, 41284, 37852, 44785, 44136, 56805 Illinois 43976, 45556, 36812, 44638, 33915, 51326, 40865, 35190, 47566, 55358 The population standard deviation for mean annual income of teachers in New York and in Illinois are estimated as 6600 and 6200, 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 New York 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. (If necessary, consult a list of formulas.) The null hypothesis: H. The alternative hypothesis: The type of test statistic: (Choose one) + The value of the test statistic: (Round to at least three decimal places.) The p-value (Round to at least three decimal places.) Can we reject the claim that the mean annual income of teachers from New York is less than or equal to the mean annual income of teachers from Illinois? Yes No

Answer 1

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