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ww-awu.aleks.com/alekscgi/x/Isl.exe/10_u-lgNslkasNW8D8A9PVVf0eU6MG8FFOW-3iCx/LnpPFQGg... Q 1$ A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Texas and Virginia. Due to recent trends

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ww-awu.aleks.com/alekscgi/x/Isl.exe/10_u-lgNslkasNW8D8A9PVVf0eU6MG8FFOW-3iCx/LnpPFQGg... Q 1$ A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Texas and Virginia. Due to recent trends in the childcare industry, the firm suspects that the mean annual income of childcare workers in Texas is less than the mean annual income of childcare workers in Virginia. To see if this is true, the firm selected a random sample of 2 childcare workers from Texas and an independent random sample of 25 childcare workers from Virginia and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars 35358, 37805 38816, 27378, 40833, 33038, 35313, 43557, 42184, 33827, 33743, 31520, 25321, 30540, 35202, 40880, 37985, 37594, Texas 26284 39948 30063 33659 41164 33494 23647 43183, 38864, 30872, 32768, 26786, 25480, 33439, 50871, 29191, 34711, 38638, 42142, 41241, 34016, 38276, 35711, 33402, 43726, Virginia 31918, 35152, 37149, 33785, 39202, 41803, 28272 Send data to calculator Send data to Excel The population standard deviation for the annual incomes of childcare workers in Texas and in Virginia are estimated as 6100 and 6300, respectively. It is also known that both populations are approximately normally distributed. At the 0.05 level of significance, is there sufficient evidence to support the claim that the mean annual income, , of childcare workers in Texas is less than the mean annual income, My of childcare workers in Virginia? 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 Hi- H :1 O (b) Determine the type of test statistic to use. (Choose one) 1020 (c) Find the value of the test statistic. (Round to three or more decimal places.) X (d) Find the critical value at the 0.05 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 Texas is less than the mean annual income of childcare workers in Virginia? OYes ONO

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