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
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 0.05 level of significance, is there sufficient evidence to support the claim that the mean annual
income, mu _(1), of childsare workers in Illinois is greater than the mean annual income, mu _(2), 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_(0) and the alternative hypothesis H_(1).
H_(0):â—»
H_(1):
(b) Determine the type of test statistic to use.
(c) Find the value of the test statistic. (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?
Yyes ONo
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
Illinois
400844389443211,48281,44348,40333,42810,44147,36122,44846 Massachusetts 39859,45095,46467,38600,3704536438,42810,41733,5606945375
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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 0.05 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, , , 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. :
u
H H
X
S
00
00
(b) Determine the type of test statistic to use.
(Choose one)
0=0
020
(c) Find the value of the test statistic. (Round to three or more decimal places.)
O>0
X
5
(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?
OYes ONo
