Question

The 2002 GSS asked respondents who they voted for in the 2000 presidential election. Among 524 female voters in the sample, 259 voted for Al Gore. Among 421 male voters in the sample, 149 voted for Gore. Is there a statistically significant gender difference in voting behavior? Alpha = 0.001

a) Is this a one-sample test or a two-sample test?
b) Is this a one-tailed test or a two-tailed test?
c) Which test statistic will you calculate?
d) Please compute the test statistic to the second decimal:
e) What is the appropriate cut-off value?
f) Is the result statistically significant? Yes/no

Answer 1

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p₁ : proportion of successes for population 1
p₂ : proportion of successes for population 2
p₁ - p₂ : Difference in proportions
H₀ : p₁ - p₂ = 0
H_A : p₁ - p₂ ? 0

Hypothesis test results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	Z-Stat	P-value
p1 - p2	259	524	149	421	0.14035557	0.032418628	4.3294729	<0.0001

Hence,

a) Two-sample

b) Two-tailed

c) z test statistic for differnce in proportions

d) Test statistic = 4.33

e) Cutoff values = -3.29, 3.29

f) Yes