MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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A tax preparation firm is interested in comparing the quality of work at two of its regional offices. The
observed frequencies showing the number of sampled returns with errors and the number of sampled
returns that were correct are as follows.
Regional Office
Return
Office 1
Office 2
Error
38
28
Correct
213
271
a. What are the sample proportions of returns with errors at the two offices?
Office 1
Office 2
p (to 2 decimals)
0.15
0.09
b. Use the chi-square test procedure to see if there is a significant difference between the population
proportion of error rates for the two offices. Test the null hypothesis H, : P1 = p2 with a .10 level of
significance. What is the p-value?
Note: We generally use the chi-square test of equal proportions when there are three or more
populations, but this example shows that the same chi-square test can be used for testing equal
proportions with two populations.
x²=
(to 3 decimals)
0.065
The p-value is between .025 and .05 ▼
What is your conclusion?
Conclude
that the two offices do not have the same population proportion error
rates.
c. A X test statistic or a z test statistic may be used to test the hypothesis. However, when we want to
make inferences about the proportions for two populations, we generally prefer the z test statistic
procedure. Comment on why the z test statistic provides the user with more options for inferences about
the proportions of two populations.
With
1.23
populations, the test statistic x will always equal z.
The z-test
is preferred because it allows for one
tailed
tests.
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Transcribed Image Text:A tax preparation firm is interested in comparing the quality of work at two of its regional offices. The observed frequencies showing the number of sampled returns with errors and the number of sampled returns that were correct are as follows. Regional Office Return Office 1 Office 2 Error 38 28 Correct 213 271 a. What are the sample proportions of returns with errors at the two offices? Office 1 Office 2 p (to 2 decimals) 0.15 0.09 b. Use the chi-square test procedure to see if there is a significant difference between the population proportion of error rates for the two offices. Test the null hypothesis H, : P1 = p2 with a .10 level of significance. What is the p-value? Note: We generally use the chi-square test of equal proportions when there are three or more populations, but this example shows that the same chi-square test can be used for testing equal proportions with two populations. x²= (to 3 decimals) 0.065 The p-value is between .025 and .05 ▼ What is your conclusion? Conclude that the two offices do not have the same population proportion error rates. c. A X test statistic or a z test statistic may be used to test the hypothesis. However, when we want to make inferences about the proportions for two populations, we generally prefer the z test statistic procedure. Comment on why the z test statistic provides the user with more options for inferences about the proportions of two populations. With 1.23 populations, the test statistic x will always equal z. The z-test is preferred because it allows for one tailed tests.
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