A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Utah and Oregon. Due to recent trends in the childcare industry, the firm suspects that the mean annual income of childcare workers in Utah is less than the mean annual income of childcare workers in Oregon. To see if this is true, the firm selected a random sample of 20 childcare workers from Utah and an independent random sample of 20 childcare workers from Oregon and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars 27060 , 42320 , 36445 , 37895 , 44564 , 35325 30313 , 28698 , 33706 , 48365 , 26946 , 25063 , 28339 , 29265 , 40051 37026 , 40150 , 42753 , 27820 , 39471 Utah 29769 , 48859 , 32480 , 36288 , 45102 , 46219 , 51098 , 45516 , 38834 , 44659 , 40755 , 38006 , 39947 , 29801 , 32200 38731 , 41370 , 28059 , 33753 35271 Oregon Send data to calc... v Send data to Excel The population standard deviation for the annual incomes of childcare workers in Utah and in Oregon are estimated as 6400 and 6500, respectively. It is also known that both populations are approximately normally distributed. At the 0.10 level of significance, is there sufficient evidence to support the claim that the mean annual income, µ1, of childcare workers in Utah is less than the mean annual income, µɔ, of childcare workers in Oregon? 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 : H, - H, = 0 H : H - H, < 0 (b) Determine the type of test statistic to use. O=0 OSO Degrees of freedom: 0 (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 Utah and Oregon. Due to recent trends in the childcare industry, the firm suspects that the mean annual income of childcare workers in Utah is less than the mean annual income of childcare workers in Oregon. To see if this is true, the firm selected a random sample of 20 childcare workers from Utah and an independent random sample of 20 childcare workers from Oregon and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars 27060 , 42320 , 36445 , 37895 , 44564 , 35325 30313 , 28698 , 33706 , 48365 , 26946 , 25063 , 28339 , 29265 , 40051 37026 , 40150 , 42753 , 27820 , 39471 Utah 29769 , 48859 , 32480 , 36288 , 45102 , 46219 , 51098 , 45516 , 38834 , 44659 , 40755 , 38006 , 39947 , 29801 , 32200 38731 , 41370 , 28059 , 33753 35271 Oregon Send data to calc... v Send data to Excel The population standard deviation for the annual incomes of childcare workers in Utah and in Oregon are estimated as 6400 and 6500, respectively. It is also known that both populations are approximately normally distributed. At the 0.10 level of significance, is there sufficient evidence to support the claim that the mean annual income, µ1, of childcare workers in Utah is less than the mean annual income, µɔ, of childcare workers in Oregon? 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 : H, - H, = 0 H : H - H, < 0 (b) Determine the type of test statistic to use. O=0 OSO Degrees of freedom: 0 (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
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Utah and Oregon. Due to
recent trends in the childcare industry, the firm suspects that the mean annual income of childcare workers in Utah is less
than the mean annual income of childcare workers in Oregon. To see if this is true, the firm selected a random sample of 20
childcare workers from Utah and an independent random sample of 20 childcare workers from Oregon and asked them to
report their mean annual income. The data obtained were as follows.
Annual income in dollars
27060 , 42320, 36445 , 37895 , 44564 , 35325 , 30313 , 28698 , 33706, 48365 , 26946 , 25063 , 28339 , 29265 , 40051
37026 , 40150, 42753
Utah
27820, 39471
29769, 48859, 32480 , 36288 45102 , 46219 , 51098 , 45516 , 38834 44659 , 40755 , 38006 , 39947 , 29801, 32200
38731 , 41370 , 28059 , 33753 , 35271
Oregon
Send data to calc... v
Send data to Excel
The population standard deviation for the annual incomes of childcare workers in Utah and in Oregon are estimated as 6400
and 6500 , respectively. It is also known that both populations are approximately normally distributed. At the 0.10 level of
significance, is there sufficient evidence to support the claim that the mean annual income, µ,, of childcare workers in Utah
ess than the mean annual income, µɔ,
childcare workers in Oregon? 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,.
p
Ho : H1 - Hy = 0
H, : H, - H, < 0
(b) Determine the type of test statistic to use.
D=0
OSO
Degrees of freedom: 0
(c) Find the value of the test statistic. (Round to three or more decimal places.)
O<O
- 1.759
|(d) Find the p-value. (Round to three or more decimal places.)
0.0433
(e) Can we support the claim that the mean annual income of childcare
workers in Utah is less than the mean annual income of childcare workers
in Oregon?
o Yes No
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman