In Calco County, 30% of the residents that vote are younger than 40 while 70% are 40 or older. A committee is interested to see if the voting habits are different in a town called Hannock. They polled 50 people who voted in the town, and of those, 20 are younger than 40 years old and 30 are 40 or older. O JMP Applet imp ? Report Distributions Distributions Ages Ages 30- Test Probabilities Level Estim Prob Hypoth Prob 0.60000 0.40000 z Test Prob > |z| 0.0039 <40 0.40000 >=40 0.60000 <40 >=40 Test Statistic -2.8868 Method: Fix hypothesized values, rescale omitted Test Probabilities Frequencies Level Estim Prob Hypoth Prob Count 20 0.40000 Level Prob 0.40000 0.30000 0.60000 0.70000 z Test Prob > |z| <40 <40 >=40 >=40 30 0.60000 Total 50 1.00000 Test Statistic 1.5430 |Method: 0.1228 N Missing 2 Levels Fix hypothesized values, rescale omitted Test Probabilities Test Probabilities Level Estim Prob Hypoth Prob Level Estim Prob Hypoth Prob 0.50000 <40 0.40000 <40 0.40000 0.20000 >=40 0.60000 0.50000 >=40 0.60000 0.80000 z Test Prob > Iz| 0.1573 Test Statistic 3.5355 0.0004 Test Statistic -1.4142 Method: Fix hypothesized values, rescale omitted Fix hypothesized values, rescale omitted Method: Count

In Calco County, 30% of the residents that vote are younger than 40 while 70% are 40 or older. A committee is interested to see if the voting habits are different in a town called Hannock. They polled 50 people who voted in the town, and of those, 20 are younger than 40 years old and 30 are 40 or older. O JMP Applet imp ? Report Distributions Distributions Ages Ages 30- Test Probabilities Level Estim Prob Hypoth Prob 0.60000 0.40000 z Test Prob > |z| 0.0039 <40 0.40000 >=40 0.60000 <40 >=40 Test Statistic -2.8868 Method: Fix hypothesized values, rescale omitted Test Probabilities Frequencies Level Estim Prob Hypoth Prob Count 20 0.40000 Level Prob 0.40000 0.30000 0.60000 0.70000 z Test Prob > |z| <40 <40 >=40 >=40 30 0.60000 Total 50 1.00000 Test Statistic 1.5430 |Method: 0.1228 N Missing 2 Levels Fix hypothesized values, rescale omitted Test Probabilities Test Probabilities Level Estim Prob Hypoth Prob Level Estim Prob Hypoth Prob 0.50000 <40 0.40000 <40 0.40000 0.20000 >=40 0.60000 0.50000 >=40 0.60000 0.80000 z Test Prob > Iz| 0.1573 Test Statistic 3.5355 0.0004 Test Statistic -1.4142 Method: Fix hypothesized values, rescale omitted Fix hypothesized values, rescale omitted Method: Count

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Description: In Calco County, 30% of the residents that vote are younger than 40 while 70% are 40 or older. A committee is interested to see if the votinghabits are different in a town called Hannock. They polled 50 people who voted in the town, and of those, 20

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.

Topic Video

Question

In Calco County, 30% of the residents that vote are younger than 40 while 70% are 40 or older. A committee is interested to see if the voting
habits are different in a town called Hannock. They polled 50 people who voted in the town, and of those, 20 are younger than 40 years old and 30
are 40 or older.
O JMP Applet
imp
?
Report
Distributions
Distributions
Ages
Ages
30
25-
Test Probabilities
20
Level
Estim Prob Hypoth Prob
0.60000
<40
0.40000
10-
>=40
0.60000
0.40000
5-
z Test Prob > Iz|
0-
Test Statistic -2.8868
<40
>a40
0.0039*
Fix hypothesized values, rescale omitted
Method:
Test Probabilities
Frequencies
Level
Estim Prob Hypoth Prob
0.30000
Level
Count
Prob
<40
0.40000
<40
20 0.40000
>=40
0.60000
0.70000
>=40
30 0.60000
z Test Prob > Iz|
Total
50
1.00000
Test Statistic 1.5430
0.1228
N Missing
2 Levels
Fix hypothesized values, rescale omitted
Method:
Test Probabilities
Test Probabilities
Level Estim Prob Hypoth Prob
Level
Estim Prob Hypoth Prob
0.20000
<40
0.40000
0.50000
<40
0.40000
>=40
0.60000
0.80000
>=40
0.60000
0.50000
z Test Prob > Iz|
z Test Prob > Iz|
Test Statistic -1.4142
0.1573
Test Statistic 3.5355
0.0004*
|Method:
Fix hypothesized values, rescale omitted
Fix hypothesized values, rescale omitted
Method:
Count

O (a)
Determine the hypothesis test to be done if the committee wants to see if the proportion of voters under 40 is different than the county
average.
Ο H,: μ< 0.7
HiiH > 0.3
Ο H: μ- 0.3
H: u = 0.3
O Ho: p > 0.3
H:p < 0.3
O H,:p = 0.3
H:p # 0.3
O Ho: p= 0.3
H:p > 0.3
(b)
Find the test statistic for the given hypothesis test. Also, find the critical value for a test with a = 0.1. (Round your answers to three decimal
places.)
test statistic
critical value
O (c)
Based on the test statistic and critical value, should the null hypothesis be accepted or rejected?
O The test statistic suggests we reject the null hypothesis; the proportion of voters younger than 40 is not statistically different in the
town.
O The test statistic suggests we fail to reject the null hypothesis; the proportion of voters younger than 40 is statistically different in the
town.
O The test statistic suggests we reject the null hypothesis; the proportion of voters younger than 40 is statistically different in the town.
O The test statistic suggests we fail to reject the null hypothesis; the proportion of voters younger than 40 is not statistically different in
the town.

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