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A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Pennsylvania and Illinois. 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 Pennsylvania is greater than the mean annual income of childcare workers in Illinois. To see if this is true, the firm selected a random sample of 20 childcare workers from Pennsylvania and an independent random sample of 20 childcare workers from Illinois and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars 53122, 46811, 48364, 39899, 43697, 52418, 46075, 48271, 52801, 44153, 50044, 55934, 53423, 50485, 46717, 46062, 57879, 49335, 48338, 51284 Pennsylvania 47815, 44961, 41642, 46003, 37293, 46568, 40751, 47488, 40654, 33919, 51710, 42108, 44896, 40813, 30789, 55215, 37858, 46357, 44480, 46594 Illinois Send data to calculator Send data to Excel The population standard deviations for the annual incomes of childcare workers in Pennsylvania and in Illinois are estimated as 6400 and 6100, respectively. It is also known that both populations are approximately normally distributed. At the 0.01 level of significance, is there sufficient evidence to support the claim that the mean annual income, ,, of childcare workers in Pennsylvania is greater than the mean annual income, u,, of childcare workers in Illinois? 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 nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Pennsylvania and Illinois. 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 Pennsylvania is greater than the mean annual income of childcare workers in Illinois. To see if this is true, the firm selected a random sample of 20 childcare workers from Pennsylvania and an independent random sample of 20 childcare workers from Illinois and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars 53122, 46811, 48364, 39899, 43697, 52418, 46075, 48271, 52801, 44153, 50044, 55934, 53423, 50485, 46717, 46062, 57879, 49335, 48338, 51284 Pennsylvania 47815, 44961, 41642, 46003, 37293, 46568, 40751, 47488, 40654, 33919, 51710, 42108, 44896, 40813, 30789, 55215, 37858, 46357, 44480, 46594 Illinois Send data to calculator Send data to Excel The population standard deviations for the annual incomes of childcare workers in Pennsylvania and in Illinois are estimated as 6400 and 6100, respectively. It is also known that both populations are approximately normally distributed. At the 0.01 level of significance, is there sufficient evidence to support the claim that the mean annual income, ,, of childcare workers in Pennsylvania is greater than the mean annual income, u,, of childcare workers in Illinois? 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.)

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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Answer letter a,b,c,d, and e on the second picture.

The population standard deviations for the annual incomes of childcare workers in Pennsylvania and in Illinois are estimated as 6400 and 6100, respectively. It is also known that both populations are approximately normally distributed. At the 0.01 level of significance, is there sufficient evidence to support the claim that the mean annual income, H, of childcare workers in Pennsylvania is greater than the mean annual income, u,, of childcare workers in Illinois? 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 H, H :0 H, 0 (b) Determine the type of test statistic to use. O=0 OSO (Choose one) v (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value at the 0.01 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? O Yias O No Dlo
Transcribed Image Text:The population standard deviations for the annual incomes of childcare workers in Pennsylvania and in Illinois are estimated as 6400 and 6100, respectively. It is also known that both populations are approximately normally distributed. At the 0.01 level of significance, is there sufficient evidence to support the claim that the mean annual income, H, of childcare workers in Pennsylvania is greater than the mean annual income, u,, of childcare workers in Illinois? 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 H, H :0 H, 0 (b) Determine the type of test statistic to use. O=0 OSO (Choose one) v (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value at the 0.01 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? O Yias O No Dlo
2 3 4 A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Pennsylvania and Illinois. 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 Pennsylvania is greater than the mean annual income of childcare workers in Illinois. To see if this is true, the firm selected a random sample of 20 childcare workers from Pennsylvania and an independent random sample of 20 childcare workers from Illinois and asked them to report their mean annual income, The data obtained were as follows. Annual income in dollars 53122, 46811, 48364, 39899, 43697, 52418, 46075, 48271, 52801, 44153, 50044, 55934, 53423, 50485, 46717, 46062, 57879, 49335 , 48338, 51284 Pennsylvania 47815, 44961, 41642, 46003, 37293, 46568, 40751, 47488, 40654, 33919, 51710, 42108, 44896, 40813, 30789, 55215, 37858, 46357, 44480, 46594 Illinois Send data to calculator Send data to Excel The population standard deviations for the annual incomes of childcare workers in Pennsylvania and in Illinois are estimated as 6400 and 6100, respectively. It is also known that both populations are approximately normally distributed. At the 0.01 level of significance, is there sufficient evidence to support the claim that the mean annual income, u,, of childcare workers in Pennsylvania is greater than the mean annual income, H, of childcare workers in Illinois? 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.)
Transcribed Image Text:2 3 4 A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Pennsylvania and Illinois. 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 Pennsylvania is greater than the mean annual income of childcare workers in Illinois. To see if this is true, the firm selected a random sample of 20 childcare workers from Pennsylvania and an independent random sample of 20 childcare workers from Illinois and asked them to report their mean annual income, The data obtained were as follows. Annual income in dollars 53122, 46811, 48364, 39899, 43697, 52418, 46075, 48271, 52801, 44153, 50044, 55934, 53423, 50485, 46717, 46062, 57879, 49335 , 48338, 51284 Pennsylvania 47815, 44961, 41642, 46003, 37293, 46568, 40751, 47488, 40654, 33919, 51710, 42108, 44896, 40813, 30789, 55215, 37858, 46357, 44480, 46594 Illinois Send data to calculator Send data to Excel The population standard deviations for the annual incomes of childcare workers in Pennsylvania and in Illinois are estimated as 6400 and 6100, respectively. It is also known that both populations are approximately normally distributed. At the 0.01 level of significance, is there sufficient evidence to support the claim that the mean annual income, u,, of childcare workers in Pennsylvania is greater than the mean annual income, H, of childcare workers in Illinois? 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.)
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