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 random sample of 25 childcare workers from Illinois and an independent random sample of 25 childcare workers from Massachusetts and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars 45679, 47412, 38478, 44646, 44364, 45265, 41423, 45861, 45936, 34016, 43020, 4960o8, 43710, 45738, 41546, 38681, 34889, 39468, 45463, 53593, 40847, 38255, 45708, 57662, 54356 Illinois 41743, 36349, 44588, 40341, 32544, 38226, 46463, 42255, 38621, 32502, 37378, 40215, 41155, 38509, 47586, 46910, 56502, Massachusetts 48907, 41861, 51211, 55186, 39078, 48263, 48059, 45771 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 0.05 level of significance, is there sufficient evidence to support the claim that the mean annual income, u,, of childcare workers in Illinois is greater than the mean annual income, Un, 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 . H, :0 H :0 (b) Determine the type of test statistic to use. (Choose one) v 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 random sample of 25 childcare workers from Illinois and an independent random sample of 25 childcare workers from Massachusetts and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars 45679, 47412, 38478, 44646, 44364, 45265, 41423, 45861, 45936, 34016, 43020, 4960o8, 43710, 45738, 41546, 38681, 34889, 39468, 45463, 53593, 40847, 38255, 45708, 57662, 54356 Illinois 41743, 36349, 44588, 40341, 32544, 38226, 46463, 42255, 38621, 32502, 37378, 40215, 41155, 38509, 47586, 46910, 56502, Massachusetts 48907, 41861, 51211, 55186, 39078, 48263, 48059, 45771 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 0.05 level of significance, is there sufficient evidence to support the claim that the mean annual income, u,, of childcare workers in Illinois is greater than the mean annual income, Un, 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 . H, :0 H :0 (b) Determine the type of test statistic to use. (Choose one) v D=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) O
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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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 Illinois is greater than the mean annual income of childcare
workers in Massachusetts. To see if this is true, the firm selected
random sample of 25 childcare workers from Illinois and an independent random sample of
25 childcare workers from Massachusetts and asked them to report their mean annual income. The data obtained were as follows.
Annual income in dollars
45679, 47412, 38478, 44646, 44364, 45265, 41423, 45861, 45936, 34016, 43020, 4960o8, 43710, 45738, 41546, 38681, 34889,
39468, 45463, 53593, 40847, 38255, 45708, 57662, 54356
Illinois
41743, 36349, 44588, 40341, 32544, 38226, 46463, 42255, 38621, 32502, 37378, 40215, 41155, 38509, 47586, 46910, 56502,
Massachusetts
48907, 41861, 51211, 55186, 39078, 48263, 48059, 45771
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 0.05 level of significance, is there sufficient evidence to support the claim that
the mean annual income, u,, of childcare workers in Illinois is greater than the mean annual income, Un, 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 .
H, :0
H :0
(b) Determine the type of test statistic to use.
(Choose one) v
D=0
OSO
(c) Find the value of the test statistic. (Round to three or more decimal places.)
O<O
(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 O No
olo
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