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". A few years ago, out of the 265 democratic senators and congressman 106 of them were in favor of a "junk food" tax. Out of the 285 republican senators and congressman only 57 of them were in favor a "junk food" tax. Based on this data, at α =.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 such a tax?

Question

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". A few years ago, out of the 265 democratic senators and congressman 106 of them were in favor of a "junk food" tax. Out of the 285 republican senators and congressman only 57 of them were in favor a "junk food" tax. Based on this data, at α =.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 such a tax?

Answer 1

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Answer 2

To determine whether the proportion of Democrats who favor a "junk food" tax is more than 5% higher than the proportion of Republicans who favor such a tax, we can conduct a hypothesis test.

Here are the steps to perform the hypothesis test:

Step 1: State the hypotheses
- Null Hypothesis (H0): p1 - p2 <= 0.05
- Alternative Hypothesis (HA): p1 - p2 > 0.05

Step 2: Set the significance level (α)
In this case, the significance level α is given as 0.01.

Step 3: Calculate the test statistic
The test statistic we will use is the z-score, given by:
z = (p̂1 - p̂2 - 0.05) / sqrt(p̂c(1 - p̂c) * (1/n1 + 1/n2))

where:
- p̂1 = proportion of Democrats in favor of a "junk food" tax = 106/265
- p̂2 = proportion of Republicans in favor of a "junk food" tax = 57/285
- p̂c = pooled proportion = (p̂1 * n1 + p̂2 * n2) / (n1 + n2)
- n1 = total number of Democrats (265)
- n2 = total number of Republicans (285)

Step 4: Calculate the critical value
The critical value represents the value beyond which we reject the null hypothesis. In this case, we want to find the critical value corresponding to a one-tailed test with a significance level of 0.01.

Step 5: Compare test statistic with critical value
If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Step 6: State the conclusion
Based on the results, we state our conclusion about the hypothesis test.

By following these steps, you can perform the hypothesis test and reach a conclusion about whether the proportion of Democrats who favor a "junk food" tax is more than 5% higher than the proportion of Republicans who favor such a tax.