A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in New York 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 New York 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 15 childcare workers from New York and an independent random sample of 15 childcare workers from Illinois and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars New York 49378, 44459, 50396, 48428, 53720, 60711, 50900, 49846, 57630, 49813, 52923, 60662, 50060, 45923, 45433 Illinois 47959, 51289, 46467, 42758, 46502, 48032, 40452, 40702, 45428, 33593, 44348, 45763, 54745, 46015, 37396 Send data to calculator Send data to Excel The population standard deviations for the annual incomes of childcare workers in New York and in Illinois are estimated as 6600 and 6200, 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, μ₁, of childcare workers in New York is greater than the mean annual income, μ₂, 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 Ho and the alternative hypothesis H₁. Ho H₁ : 0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) μ ローロ S □□ □<ロ (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 New York is greater than the mean annual income of childcare workers in Illinois? Vec No
A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in New York 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 New York 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 15 childcare workers from New York and an independent random sample of 15 childcare workers from Illinois and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars New York 49378, 44459, 50396, 48428, 53720, 60711, 50900, 49846, 57630, 49813, 52923, 60662, 50060, 45923, 45433 Illinois 47959, 51289, 46467, 42758, 46502, 48032, 40452, 40702, 45428, 33593, 44348, 45763, 54745, 46015, 37396 Send data to calculator Send data to Excel The population standard deviations for the annual incomes of childcare workers in New York and in Illinois are estimated as 6600 and 6200, 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, μ₁, of childcare workers in New York is greater than the mean annual income, μ₂, 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 Ho and the alternative hypothesis H₁. Ho H₁ : 0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) μ ローロ S □□ □<ロ (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 New York is greater than the mean annual income of childcare workers in Illinois? Vec No
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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Transcribed Image Text:A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in New York 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 New York 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 15 childcare workers from New York and an independent random sample
of 15 childcare workers from Illinois and asked them to report their mean annual income. The data obtained were as follows.
Annual income in dollars
New York 49378, 44459, 50396, 48428, 53720, 60711, 50900, 49846, 57630, 49813, 52923, 60662, 50060, 45923, 45433
Illinois 47959, 51289, 46467, 42758, 46502, 48032, 40452, 40702, 45428, 33593, 44348, 45763, 54745, 46015, 37396
Send data to calculator
Send data to Excel
The population standard deviations for the annual incomes of childcare workers in New York and in Illinois are estimated as 6600 and 6200, 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, μ₁, of childcare workers in New York is greater than the mean annual income, μ₂, 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 Ho and the alternative hypothesis H₁.
Ho
H₁ : 0
(b) Determine the type of test statistic to use.
(Choose one)
(c) Find the value of the test statistic. (Round to three or more decimal places.)
μ
ローロ
S
□□
□<ロ
(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 New York is
greater than the mean annual income of childcare workers in Illinois?
Vec No
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