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?
The information and statements you have provided are not relevant to the given data about male and female voter participation in an election. Therefore, it is not possible to determine if participation in the election is the same for males and females based on the information provided.
To determine whether participation in the election is the same for males and females, we can conduct a hypothesis test.
Null Hypothesis (H0): The proportion of male voters who participated in the election is equal to the proportion of female voters who participated in the election.
Alternative Hypothesis (H1): The proportion of male voters who participated in the election is not equal to the proportion of female voters who participated in the election.
Let's calculate the proportions:
Proportion of male voters who participated in the election (p1) = 850 / (850 + 750) = 0.531
Proportion of female voters who participated in the election (p2) = 1024 / (1024 + 976) = 0.512
We can now perform a two-sample proportion test using these proportions to determine if there is a significant difference between the participation rates of males and females.
Under the null hypothesis, the difference between the proportions (p1 - p2) should be 0.
The test statistic for this hypothesis test is calculated as follows:
Z = (p1 - p2) / sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))
where n1 and n2 are the sample sizes for males and females, respectively.
Let's assume the sample sizes were 1600 for both males and females (800 males and 800 females).
Z = (0.531 - 0.512) / sqrt((0.531 * (1 - 0.531) / 800) + (0.512 * (1 - 0.512) / 800))
= 0.019 / sqrt(0.000934 + 0.000956)
= 0.019 / sqrt(0.00189)
= 0.019 / 0.0434
= 0.437
The critical Z-value for a significance level of 0.05 (α = 0.05) is approximately ±1.96 (two-tailed test).
Since the calculated Z-value (0.437) is within the range of -1.96 and 1.96, we fail to reject the null hypothesis.
Therefore, based on the given data, we do not have sufficient evidence to conclude that participation in the election is different for males and females.