A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Texas and Virginia. Due to recent trends in the childcare industry, the firm suspects that the mean annual income of childcare workers in Texas is less than the mean annual income of childcare workers in Virginia. To see if this is true, the firm selected a random sample of 10 childcare workers from Texas and an independent random sample of 10 childcare workers from Virginia and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars Texas 26950, 39167, 36383, 37183, 46661, 39149, 36562, 32419, 21419, 39430 Virginia 33493, 27316, 38616, 42893, 35369, 34236, 30451, 32245, 42865, 32494| Send data to calculator Send data to Excel The population standard deviation for the annual incomes of childcare workers in Texas and in Virginia are estimated as 6100 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, µ, of childcare workers in Texas is less than the mean annual income, H2, of childcare workers in Virginia? 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) O=0 OSO
A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Texas and Virginia. Due to recent trends in the childcare industry, the firm suspects that the mean annual income of childcare workers in Texas is less than the mean annual income of childcare workers in Virginia. To see if this is true, the firm selected a random sample of 10 childcare workers from Texas and an independent random sample of 10 childcare workers from Virginia and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars Texas 26950, 39167, 36383, 37183, 46661, 39149, 36562, 32419, 21419, 39430 Virginia 33493, 27316, 38616, 42893, 35369, 34236, 30451, 32245, 42865, 32494| Send data to calculator Send data to Excel The population standard deviation for the annual incomes of childcare workers in Texas and in Virginia are estimated as 6100 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, µ, of childcare workers in Texas is less than the mean annual income, H2, of childcare workers in Virginia? 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) O=0 OSO
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 Texas and Virginia. Due to recent trends in the childcare industry,
the firm suspects that the mean annual income of childcare workers in Texas is less than the mean annual income of childcare workers in Virginia. To see if this
is true, the firm selected a random sample of 10 childcare workers from Texas and an independent random sample of 10 childcare workers from Virginia and
asked them to report their mean annual income. The data obtained were as follows.
Annual income in dollars
Техas
26950, 39167, 36383, 37183, 46661, 39149, 36562, 32419, 21419, 39430
Virginia 33493, 27316, 38616, 42893, 35369, 34236, 30451, 32245, 42865, 32494
Send data to calculator
Send data to Excel
The population standard deviation for the annual incomes of childcare workers in Texas and in Virginia are estimated as 6100 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 Texas is less than the mean annual income, µ,, of childcare workers in Virginia? 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, :
H :0
(b) Determine the type of test statistic to use.
|(Choose one)
D=0
OSO
Transcribed Image Text:(a) State the null hypothesis H, and the alternative hypothesis H .
Ho
H, :0
(b) Determine the type of test statistic to use.
D=0
OSO
(Choose one)
O#0
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 Texas is less than the mean annual income of childcare workers in
Virginia?
OYes ONo
미□
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