How to solve please show step by step EspañolA nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Texas and Indiana. 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 Indiana. To see if thisis true, the firm selected a random sample of 25 childcare workers from Texas and an independent random sample of 25 childcare workers from Indiana andasked them to report their mean annual income. The data obtained were as follows.Annual income in dollarsTexas30111, 35543, 34245, 42733, 40077, 25500, 35332, 28216, 38243, 37548, 34262, 31505, 37073, 31673, 33941, 32640, 27860, 29796,32562, 39692, 35943, 40878, 48072, 29502, 32661Indiana42600, 30305, 34336, 42456, 34420, 30744, 38497, 38950, 40314, 32071, 37746, 43031, 37645, 41701, 43402, 33090, 39851, 36107,45694, 32670, 39027, 39030, 43787, 44748, 40842Send data to calculator VSend data to ExcelAaThe population standard deviation for the annual incomes of childcare workers in Texas and in Indiana are estimated as 6200 and 6500, respectively. It is alsoknown that both populations are approximately normally distributed. At the 0.01 level of significance, is there sufficient evidence to support the claim that themean annual income, μ₁, of childcare workers in Texas is less than the mean annual income, μ2, of childcare workers in Indiana? Perform a one-tailed test. Thencomplete 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.OрSHoH₁ :0(b) Determine the type of test statistic to use.0=0 ☐≤O 0²0(Choose one) ▼(c) Find the value of the test statistic. (Round to three or more decimal places.)☐#0 0OXŚ(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 workersin Texas is less than the mean annual income of childcare workers inExplanationCheck© 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility$103|xX 20The population standard deviation for the annual incomes of childcare workers in Texas and in Indiana are estimated as 6200 and 6500, respectively. It is alsoknown that both populations are approximately normally distributed. At the 0.01 level of significance, is there sufficient evidence to support the claim that themean annual income, μ₁, of childcare workers in Texas is less than the mean annual income, μ₂, of childcare workers in Indiana? Perform a one-tailed test. Thencomplete 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.OРAaHo:SH₁ :0(b) Determine the type of test statistic to use.OSO020(Choose one)(c) Find the value of the test statistic. (Round to three or more decimal places.)000Ś?(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 workersin Texas is less than the mean annual income of childcare workers inIndiana?Yes No2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | AccessibilityExplanationCheck3XI0#0X

Question

How to solve please show step by step EspañolA nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Texas and Indiana. 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 Indiana. To see if thisis true, the firm selected a random sample of 25 childcare workers from Texas and an independent random sample of 25 childcare workers from Indiana andasked them to report their mean annual income. The data obtained were as follows.Annual income in dollarsTexas30111, 35543, 34245, 42733, 40077, 25500, 35332, 28216, 38243, 37548, 34262, 31505, 37073, 31673, 33941, 32640, 27860, 29796,32562, 39692, 35943, 40878, 48072, 29502, 32661Indiana42600, 30305, 34336, 42456, 34420, 30744, 38497, 38950, 40314, 32071, 37746, 43031, 37645, 41701, 43402, 33090, 39851, 36107,45694, 32670, 39027, 39030, 43787, 44748, 40842Send data to calculator VSend data to ExcelAaThe population standard deviation for the annual incomes of childcare workers in Texas and in Indiana are estimated as 6200 and 6500, respectively. It is alsoknown that both populations are approximately normally distributed. At the 0.01 level of significance, is there sufficient evidence to support the claim that themean annual income, μ₁, of childcare workers in Texas is less than the mean annual income, μ2, of childcare workers in Indiana? Perform a one-tailed test. Thencomplete 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.OрSHoH₁ :0(b) Determine the type of test statistic to use.0=0 ☐≤O 0²0(Choose one) ▼(c) Find the value of the test statistic. (Round to three or more decimal places.)☐#0 0<0 ☐>OXŚ(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 workersin Texas is less than the mean annual income of childcare workers inExplanationCheck© 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility$103|xX 20The population standard deviation for the annual incomes of childcare workers in Texas and in Indiana are estimated as 6200 and 6500, respectively. It is alsoknown that both populations are approximately normally distributed. At the 0.01 level of significance, is there sufficient evidence to support the claim that themean annual income, μ₁, of childcare workers in Texas is less than the mean annual income, μ₂, of childcare workers in Indiana? Perform a one-tailed test. Thencomplete 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.OРAaHo:SH₁ :0(b) Determine the type of test statistic to use.OSO020(Choose one)(c) Find the value of the test statistic. (Round to three or more decimal places.)0<0 0>00Ś?(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 workersin Texas is less than the mean annual income of childcare workers inIndiana?Yes No2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | AccessibilityExplanationCheck3XI0#0X

Accepted Answer

Given that:

Annual income in dollars

Texas
30111, 35543, 34245,42733, 40077, 25500, 35332,…