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.)Given that alpha is .05, the conclusion isGroup of answer choicesrevise hoNo answer text provided.do not reject horeject ho
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.)Given that alpha is .05, the conclusion isGroup of answer choicesrevise hoNo answer text provided.do not reject horeject ho
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).
Step 4: Interpret the results. We use the Normal Distribution to find the probability that a z-score is less than the observed test statistic (the p-value). If the p-value is less than the significance level (alpha), we reject the null hypothesis.
Without the actual calculations and the resulting p-value, we can't definitively say whether to reject or not reject the null hypothesis. However, if the p-value is less than alpha (.05), we would reject the null hypothesis and conclude that there is a significant difference between the proportions of females and males who plan to vote for the incumbent president. If the p-value is greater than alpha, we would not reject the null hypothesis.
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