You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 59% at a level of significance of αα = 0.05. According to your sample, 52 out of 89 potential voters prefer the Democratic candidate.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 59% at a level of significance of αα = 0.05. According to your sample, 52 out of 89 potential voters prefer the Democratic candidate.

Expert Solution
Step 1

Given: n = 89, x = 52, α = 0.05, p = 0.59.

Sample proportion:

p^=xn=5289=0.5843

 

 

Step 2

Hypothesis to be tested:

H0:p=p0H1:p<p0

Test statistic:

z=p^-p0p01-p0n=0.5843-0.590.591-0.5989=-0.11

Critical value for this left tailed test at α = 0.05 is Zc = -1.64.

 

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