Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)(a)State the null hypothesis H0 and the alternative hypothesis H1.H0:H1:(b)Determine the type of test statistic to use. ▼(Choose one) (c)Find the value of the test statistic. (Round to three or more decimal places.) (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 Pennsylvania is greater than the mean annual income of childcare workers in Illinois? A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Pennsylvania and Illinois. Due to recent trends in the childcareindustry, the firm suspects that the that the mean annual income of childcare workers in the state of Pennsylvania is greater than the mean annual income ofchildcare workers in Illinois. To see if this is true, the firm selected a random sample of 15 childcare workers from Pennsylvania and an independent randomsample of 15 childcare workers from Illinois and asked them to report their mean annual income. The data obtained were as follows.Annual income in dollarsPennsylvania 54197, 46594, 57237, 43530, 41792, 48612, 46584, 54266, 53218, 56269, 52335, 53235, 53330, 42217, 36717Illinois49027, 45540, 40256, 43444, 31079, 45096, 56638, 45390, 54321, 48214, 44924, 38383, 50672, 35447, 46545Send data to calculatorSend data to ExcelThe population standard deviations for the annual incomes of childcare workers in Pennsylvania and in Illinois are estimated as 6400 and 6100, respectively. It isalso known that both populations are approximately normally distributed. At the 0.10 level of significance, is there sufficient evidence to support the claim thatthe mean annual income, u,, of childcare workers in Pennsylvania is greater than the mean annual income, µ, of childcare workers in Illinois? Perform a one-tailed test. Then complete the parts below.

Name: Carry your intermediate computations to at least three decimal places.
Uploaded: 2024-03-20T07:07:12.000Z
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Description: Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)(a)State the null hypothesis H0 and the alternative hypothesis H1.H0:H1:(b)Determine the type of test statistic to use. ▼(Choose one) (c

Question

Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)(a)State the null hypothesis H0 and the alternative hypothesis H1.H0:H1:(b)Determine the type of test statistic to use. ▼(Choose one) (c)Find the value of the test statistic. (Round to three or more decimal places.) (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 Pennsylvania is greater than the mean annual income of childcare workers in Illinois? A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Pennsylvania and Illinois. Due to recent trends in the childcareindustry, the firm suspects that the that the mean annual income of childcare workers in the state of Pennsylvania is greater than the mean annual income ofchildcare workers in Illinois. To see if this is true, the firm selected a random sample of 15 childcare workers from Pennsylvania and an independent randomsample of 15 childcare workers from Illinois and asked them to report their mean annual income. The data obtained were as follows.Annual income in dollarsPennsylvania 54197, 46594, 57237, 43530, 41792, 48612, 46584, 54266, 53218, 56269, 52335, 53235, 53330, 42217, 36717Illinois49027, 45540, 40256, 43444, 31079, 45096, 56638, 45390, 54321, 48214, 44924, 38383, 50672, 35447, 46545Send data to calculatorSend data to ExcelThe population standard deviations for the annual incomes of childcare workers in Pennsylvania and in Illinois are estimated as 6400 and 6100, respectively. It isalso known that both populations are approximately normally distributed. At the 0.10 level of significance, is there sufficient evidence to support the claim thatthe mean annual income, u,, of childcare workers in Pennsylvania is greater than the mean annual income, µ, of childcare workers in Illinois? Perform a one-tailed test. Then complete the parts below.

Accepted Answer

Given Data :

For Sample 1

x̄1 = 49342.2

σ1 = 6400.0

n1 = 15

For Sample…