True or False: Citizen registration and voting varies by age and gender. The fol
ID: 2908442 • Letter: T
Question
True or False:
Citizen registration and voting varies by age and gender. The following data is based on registration and voting results from the Current Population Survey following the 2012 election. A survey was conducted of adults eligible to vote. The respondents were asked in they registered to vote. The data below are based on a total sample of 760. We will focus on the proportion registered to vote for ages 18 to 24 compared with those 25 to 34. The expectation is that registration is lower for the younger age group. The data are given below.
We conduct a difference of proportion test between persons 18 to 24 minus persons 25 to 34, where the null hypothesis is that the difference is zero. The test statistic is -1.9365. Based on an alpha level of .05 for a one-tailed test where the proportion for those 18 to 24 is lower, you can conclude that there is a significant difference.
Explanation / Answer
Solution:- False.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P1> P2
Alternative hypothesis: P1 < P2
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
z = (p1 - p2) / SE
z = - 1.94
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a one-tailed test, the P-value is the probability that the z-score is less than -1.94
Thus, the P-value = 0.026.
Interpret results. Since the P-value (0.026) is greater than the significance level (0.05), we cannot reject the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that registration is lower for the younger age group.
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