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 workersin 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 20 childcare workers from Illinois and an independent random sample of 20 childcareworkers from Massachusetts and asked them to report their mean annual income. The data obtained were as follows.Annual income in dollars37896, 50812, 42944, 45727, 43304, 52847, 43622, 42464, 47874, 44955, 47674, 48239, 55083, 36382, 48214,Illinois46704, 48523, 53463, 31679, 3497541237, 53288, 43667, 43092, 39306, 49712, 51263, 42971, 46154, 52665, 46595, 43768, 36185, 37979, 33292,Massachusetts54628, 46888, 43504, 43334, 48774Send data to calc... vThe population standard deviations for the annual incomes of childcare workers in Illinois and in Massachusetts areestimated as 6200 and 6300, respectively. It is also known that both populations are approximately normally distributed. Atthe 0.01 level of significance, is there sufficient evidence to support the claim that the mean annual income, µ,of childcareworkers in Illinois is greater than the mean annual income, µ, of childcare workers in Massachusetts? Perform a one-tailedtest. 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.Ho :0H1 :0(b) Determine the type of test statistic to use.D=0OSO(Choose one)O

Name: A nationwide job recruiting firm wants to compare the annual incomes
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Description: 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 workersin th

Solution: Given information: n1=20 Sample size of Illinoisn2= 20 Sample size of…

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 20 childcare workers from Illinois and an independent random sample of 20 childcare workers from Massachusetts and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars 37896, 50812, 42944, 45727, 43304, 52847, 43622, 42464, 47874, 44955, 47674, 48239, 55083, 36382, 48214, Illinois 46704, 48523, 53463, 31679, 34975 | 41237, 53288, 43667, 43092, 39306, 49712, 51263, 42971, 46154, 52665, 46595, 43768, 36185, 37979, 33292, 54628, 46888, 43504, 43334, 48774 Massachusetts Send data to calc... ♥ 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 0.01 level of significance, is there sufficient evidence to support the claim that the mean annual income, of childcare workers in Illinois is greater than the mean annual income, µ, 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 H,. Ho :0 H1 :0 (b) Determine the type of test statistic to use. D=0 OSO (Choose one) O

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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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 20 childcare workers from Illinois and an independent random sample of 20 childcare
workers from Massachusetts and asked them to report their mean annual income. The data obtained were as follows.
Annual income in dollars
37896, 50812, 42944, 45727, 43304, 52847, 43622, 42464, 47874, 44955, 47674, 48239, 55083, 36382, 48214,
Illinois
46704, 48523, 53463, 31679, 34975
41237, 53288, 43667, 43092, 39306, 49712, 51263, 42971, 46154, 52665, 46595, 43768, 36185, 37979, 33292,
Massachusetts
54628, 46888, 43504, 43334, 48774
Send data to calc... v
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 0.01 level of significance, is there sufficient evidence to support the claim that the mean annual income, µ,
of childcare
workers in Illinois is greater than the mean annual income, µ, 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.
Ho :0
H1 :0
(b) Determine the type of test statistic to use.
D=0
OSO
(Choose one)
O<O
(c) Find the value of the test statistic. (Round to three or more decimal places.)
?
(d) Find the p-value. (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 No
olo

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