A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in New York and Illinois. Due to recent trends in the childcare industry, the firm suspects that the that the mean annual income of childcare workers in the ? state of New York is greater than the mean annual income of childcare workers in Illinois. To see if this is true, the firm selected a random sample of 15 childcare workers from New York and an independent random sample of 15 childcare workers from Illinois and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars New York 48205, 49959, 56823, 49383, 46878, 44282, 47622, 46516, $7321, 52102, 51762, 42289, 51587, 55176, 45878 Illinois 54099, 43487, 42438, 41940, 40871, 38783, 46709, 41399. 37590, 40647. 54173, 48386, 48379, 46382, 50093 Send data to calc... v Send data to Excel The population standard deviations for the annual incomes of childcare workers 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 0.10 level of significance, is there sufficient evidence to support the claim that the mean annual income, p, of childcare workers in New York is greater than the mean annual income, p2, of childcare workers in Illinois? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis // and the alternative hypothesis //, Ho :D # :D (b) Determine the type of test statistic to use. Degrees of freedom: " (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we support the claim that the mean annual income of childcare workers in New York is greater than the mean annual income of childcare workers in Illinois? Yes No