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.9115.80.177.0885

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 (There is no difference in voting proportions between females and males) Alternative hypothesis: p1 ≠ p2 (There is a difference in voting proportions between females and males)

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 in proportions could have happened by chance under the null hypothesis.

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).

• Number of successes for females (x1) = 120, sample size for females (n1) = 300
• Number of successes for males (x2) = 140, sample size for males (n2) = 400

The pooled sample proportion is p = (x1 + x2) / (n1 + n2) = (120 + 140) / (300 + 400) = 260 / 700 = 0.3714

The standard error is SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] } = sqrt{ 0.3714 * ( 1 - 0.3714 ) * [ (1/300) + (1/400) ] } = 0.0286

The z-score is z = (p1 - p2) / SE = (120/300 - 140/400) / 0.0286 = -0.05 / 0.0286 = -1.748

Step 4: Interpret the results. We use the Normal Distribution Calculator to find the probability that a z-score is less than -1.748. The calculator tells us that P(Z < -1.748) = 0.0401. Because this p-value (0.0401) is less than the significance level (0.05), we cannot accept the null hypothesis. Therefore, we conclude that there is a significant difference between the proportions of females and males who plan to vote for the incumbent president.

So, the correct answer is none of the provided options. The calculated p-value is 0.0401.

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 = 1.5625

Step 4: Interpret the results. We use the Normal Distribution to find the probability that a z-score is less than 1.5625 (this is the p-value). If the p-value is less than the significance level (alpha = .05), we reject the null hypothesis.

The p-value is 0.1186 (from z-table or software). Since the p-value (0.1186) is greater than the significance level (0.05), we cannot reject the null hypothesis.

So, the correct answer from the given choices is 0.1186. However, none of the provided options match this result. Please check the question or the provided options.