Of 300 female registered voters surveyed, 120 indicated they were planning to vote for the incumbent president; while of 400 male registered voters, 140 indicated they were planning to vote for the incumbent president. At alpha = .05, test to see if there is a significant difference between the proportions of females and males who plan to vote for the incumbent president. (Use the p-value approach.)Determine the pvalueGroup of answer choices.0885.80.177.9115
Question
Of 300 female registered voters surveyed, 120 indicated they were planning to vote for the incumbent president; while of 400 male registered voters, 140 indicated they were planning to vote for the incumbent president. At alpha = .05, test to see if there is a significant difference between the proportions of females and males who plan to vote for the incumbent president. (Use the p-value approach.)Determine the pvalueGroup of answer choices.0885.80.177.9115
Solution
To answer this question, we need to conduct a hypothesis test for the difference between two proportions. Here are the steps:
Step 1: State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: p1 = p2 (The proportion of females who plan to vote for the incumbent president is equal to the proportion of males who plan to vote for the incumbent president)
Alternative hypothesis: p1 ≠ p2 (The proportion of females who plan to vote for the incumbent president is not equal to the proportion of males who plan to vote for the incumbent president)
Step 2: Formulate an analysis plan. For this analysis, the significance level is defined as alpha = .05. We will use a two-proportion z-test to determine whether the observed difference between the proportions is statistically significant.
Step 3: 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).
p1 = 120/300 = 0.4 (proportion of females) p2 = 140/400 = 0.35 (proportion of males)
p = (p1 * n1 + p2 * n2) / (n1 + n2) = (0.4 * 300 + 0.35 * 400) / (300 + 400) = 0.3722
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] } = sqrt{ 0.3722 * (1 - 0.3722) * [ (1/300) + (1/400) ] } = 0.032
z = (p1 - p2) / SE = (0.4 - 0.35) / 0.032 = 1.56
Step 4: Interpret the results. We use the Normal Distribution to find the probability that a z-score is less than 1.56, which is 0.0594. However, because our test is two-tailed, we need to multiply this by 2, which gives us a p-value of 0.1188.
Since the p-value (0.1188) is greater than the significance level (0.05), we cannot reject the null hypothesis. There is not enough evidence to say that there is a significant difference between the proportions of females and males who plan to vote for the incumbent president.
So, the closest answer choice to our calculated p-value is 0.177.
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