A candidate for political office wants to determine if there is a difference in
ID: 3225117 • Letter: A
Question
A candidate for political office wants to determine if there is a difference in his popularity between men and women. To test the claim of this difference, he conducts a survey of voters. The sample contains 250 men and 250 women, of which 44% of the men and 52% of the women favor his candidacy. Do these values indicate a difference in popularity? Use a 0.01 significance level. What are the hypothesis statements? H_o: P_m =P_w H_A: P_m > P_w H_o: P_m = P_w H_A: P_m notequalto P_w H_o: P_m = P_w H_A: P_mExplanation / Answer
Hypothesis statements are
H0: pm=pw
HA: pmpw
Questioon-8
From following results Z=1.79 and p=0.0734
Z Test for Differences in Two Proportions
Data
Hypothesized Difference
0
Level of Significance
0.01
Group 1
Number of Successes
110
Sample Size
250
Group 2
Number of Successes
130
Sample Size
250
Intermediate Calculations
Group 1 Proportion
0.44
Group 2 Proportion
0.52
Difference in Two Proportions
-0.08
Average Proportion
0.48
Z Test Statistic
-1.790287185
Two-Tail Test
Lower Critical Value
-2.575829304
Upper Critical Value
2.575829304
p-Value
0.073407755
Do not reject the null hypothesis
Questioon-9
As p-value>0.01, we do not reject the null hypothesis and hence there is no difference in popularity
Z Test for Differences in Two Proportions
Data
Hypothesized Difference
0
Level of Significance
0.01
Group 1
Number of Successes
110
Sample Size
250
Group 2
Number of Successes
130
Sample Size
250
Intermediate Calculations
Group 1 Proportion
0.44
Group 2 Proportion
0.52
Difference in Two Proportions
-0.08
Average Proportion
0.48
Z Test Statistic
-1.790287185
Two-Tail Test
Lower Critical Value
-2.575829304
Upper Critical Value
2.575829304
p-Value
0.073407755
Do not reject the null hypothesis
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