Let p₁ represent the population proportion of U.S.Senate and Congress (House of Representatives)democrats who are in favor of a new modest tax on "junk food".Let p₂ represent the population proportion of U.S.Senate and Congress (House of Representative)republicans who are in favor of a new modest tax on "junk food".Out of the 265 democratic senators and congressman 106 of them are in favor of a "junk food" tax.Out of the 285 republican senators and congressman only 57 of them are in favor of a "junk food" tax.At = .01,can we conclude that the proportion of democrats who favor "junk food" tax is more than 5% higher than proportion of republicans who favor the new tax? A)Yes B)No

Question

Quizplus · Accepted Answer

First, we need to calculate the sample proportions of democrats and republicans who favor the tax:

$\hat{p}_1 = \frac{106}{265} \approx 0.4$

$\hat{p}_2 = \frac{57}{285} \approx 0.2$

Next, we need to calculate the difference in sample proportions:

$\hat{p}_1 - \hat{p}_2 = 0.4 - 0.2 = 0.2$

Now, we need to calculate the standard error of the difference in sample proportions:

$SE = \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$

$SE = \sqrt{\frac{0.4(1-0.4)}{265} + \frac{0.2(1-0.2)}{285}} \approx 0.048$

Finally, we can calculate the z-score:

$z = \frac{\hat{p}_1 - \hat{p}_2 - 0.05}{SE} = \frac{0.2 - 0.05}{0.048} \approx 3.12$

Since the calculated z-score is greater than the critical z-value of 2.33 (at 0.01 significance level), we can reject the null hypothesis that the proportion of democrats who favor the tax is not more than 5% higher than the proportion of republicans who favor the tax. Therefore, we can conclude that the proportion of democrats who favor the tax is more than 5% higher than the proportion of republicans who favor the tax.

Let P1 Represent the Population Proportion of U

Let P₁ Represent the Population Proportion of U