Hypothesis test A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Utah and Oregon. Due to recent trends in the childcare industry, the firm suspects that the mean annual income of childcare workers in Utah is less than the mean annual income of childcare workers in Oregon. To see if this is true, the firm selected a random sample of 10 childcare workers from Utah and an independent random sample of 10 childcare workers from Oregon and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars Utah 33256, 35031, 32839, 30763, 36516, 26715, 35376, 32557, 37763, 19182 Oregon 46808, 28622, 45590, 36543, 38397, 42273, 36705, 46441, 37382, 39051 Send data to calculator Send data to Excel The population standard deviation for the annual incomes of childcare workers in Utah and in Oregon are estimated as 6400 and 6500, 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, H, of childcare workers in Utah is less than the mean annual income, H2, of childcare workers in Oregon? 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 Ho and the alternative hypothesis H1. O H : I X S H, : 0 (b) Determine the type of test statistic to use. (Choose one) V 0=0 OSO 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0*0 00 X ? (d) Find the critical value at the 0.10 level of significance. (Round to three or more decimal places.) (e) Can we support the claim that the mean annual income of childcare workers in Utah is less than the mean annual income of childcare workers in Oregon? Yes No