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A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Illinois and Massachusetts. 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 Illinois is greater than the mean annual income of childcare workers in Massachusetts. To see if this is true, the firm selected a random sample of 10 childcare workers from Illinois and an independent random sample of 10 childcare workers from Massachusetts and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars 47834, 49703, 34814, 41101, 54947, 33493, 40760, 47811, 46876, 37958 Massachusetts 41509, 52059, 39518, 52393, 41426, 38522, 50917, 51090, 40711, 52998 | Illinois Send data to calculator Send data to Excel The population standard deviations for the annual incomes of childcare workers in Illinois and in Massachusetts are estimated as 6200 and 6300, 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 dlaim that the mean annual income, H1, of childcare workers in Illinois is greater than the mean annual income, 42, of childcare workers in Massachusetts? 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 H, and the alternative hypothesis H1. H, :0 H :0 |(b) Determine the type of test statistic to use. D=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) O

A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Illinois and Massachusetts. 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 Illinois is greater than the mean annual income of childcare workers in Massachusetts. To see if this is true, the firm selected a random sample of 10 childcare workers from Illinois and an independent random sample of 10 childcare workers from Massachusetts and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars 47834, 49703, 34814, 41101, 54947, 33493, 40760, 47811, 46876, 37958 Massachusetts 41509, 52059, 39518, 52393, 41426, 38522, 50917, 51090, 40711, 52998 | Illinois Send data to calculator Send data to Excel The population standard deviations for the annual incomes of childcare workers in Illinois and in Massachusetts are estimated as 6200 and 6300, 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 dlaim that the mean annual income, H1, of childcare workers in Illinois is greater than the mean annual income, 42, of childcare workers in Massachusetts? 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 H, and the alternative hypothesis H1. H, :0 H :0 |(b) Determine the type of test statistic to use. D=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) O

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Illinois and Massachusetts. 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 Ilinois is greater than the mean annual income of childcare workers in Massachusetts. To see if this is true, the firm selected a random sample of 10 childcare workers from Illinois and an independent random sample of 10 childcare workers from Massachusetts and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars 47834, 49703, 34814, 41101, 54947, 33493, 40760, 47811, 46876, 37958 Massachusetts 41509, 52059, 39518, 52393, 41426, 38522, 50917, 51090, 40711, 52998 Send data to Excel Illinois Send data to calculator The population standard deviations for the annual incomes of childcare workers in Illinois and in Massachusetts are estimated as 6200 and 6300, 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 daim that the mean annual income, l1, of childcare workers in Illinois is greater than the mean annual income, Hz, of childcare workers in Massachusetts? 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 H, and the alternative hypothesis H1. H, :0 H :0 (b) Determine the type of test statistic to use. O=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) O<O ? (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 Illinois is greater than the mean annual income of childcare workers in Massachusetts? O Yes O No
Transcribed Image Text:A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Illinois and Massachusetts. 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 Ilinois is greater than the mean annual income of childcare workers in Massachusetts. To see if this is true, the firm selected a random sample of 10 childcare workers from Illinois and an independent random sample of 10 childcare workers from Massachusetts and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars 47834, 49703, 34814, 41101, 54947, 33493, 40760, 47811, 46876, 37958 Massachusetts 41509, 52059, 39518, 52393, 41426, 38522, 50917, 51090, 40711, 52998 Send data to Excel Illinois Send data to calculator The population standard deviations for the annual incomes of childcare workers in Illinois and in Massachusetts are estimated as 6200 and 6300, 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 daim that the mean annual income, l1, of childcare workers in Illinois is greater than the mean annual income, Hz, of childcare workers in Massachusetts? 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 H, and the alternative hypothesis H1. H, :0 H :0 (b) Determine the type of test statistic to use. O=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) O<O ? (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 Illinois is greater than the mean annual income of childcare workers in Massachusetts? O Yes O No
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