Assume all samples are simple random samples and α (alpha) is taken to be 0.05.
In a certain city, there are about 250,000 eligible voters. A sample of male voters and a sample of female voters were taken to study the relationship between sex and participation in the last election. The results:
Men that voted 850
Women that voted 1024
Men that didn’t vote 750
Women that didn’t vote 976
Is participation in the election the same for males and females?
Question 1 options:
1)
One sample z-test for the population mean.
2)
two sample z-test for the population means.
3)
One sample z-test for proportions.
4)
two sample z-test for proportions.
5)
one sample t-test for the population mean.
6)
None of our hypothesis tests fit.
The appropriate hypothesis test to determine if participation in the election is the same for males and females would be a two sample z-test for proportions.
In this case, the null hypothesis would be that the proportion of male voters is equal to the proportion of female voters. The alternative hypothesis would be that the proportions are not equal.
The test statistic for a two sample z-test for proportions can be calculated using the formula:
z = (p1 - p2) / sqrt( (p̂ * (1-p̂) / n1) + (p̂ * (1-p̂) / n2) )
where:
p1 = proportion of males who voted
p2 = proportion of females who voted
p̂ = combined proportion of voters ( (850 + 1024) / (850 + 750 + 1024 + 976) )
n1 = sample size for males (850 + 750)
n2 = sample size for females (1024 + 976)
The critical value for a 0.05 significance level in a two-tailed test is approximately 1.96.
If the absolute value of the calculated test statistic is greater than 1.96, then we would reject the null hypothesis and conclude that participation in the election is different for males and females. Otherwise, we would fail to reject the null hypothesis and conclude that there is no significant difference in participation between males and females.