Question 1

Let [latex]p_{1}[/latex] be the true proportion (written as a decimal) of U.S. women who considered themselves to be vegetarian. On the following number line, sketch and label an interval that contains all the possible values for [latex]p_{1}[/latex].

Question 2

Let [latex]p_{2}[/latex] be the true proportion (written as a decimal) of U.S. men who considered themselves to be vegetarian. On the following number line, sketch and label an interval that contains all the possible values for [latex]p_{2}[/latex].

Question 3

On the following number line, sketch and label an interval that contains all the possible values for [latex]p_{1} - p_{2}[/latex].

Question 4

The Gallup survey that was mentioned at the beginning of this corequisite support activity found that 6% of U.S. adult women surveyed considered themselves to be vegetarian and 4% of U.S. adult men surveyed considered themselves to be vegetarian.^[1]

1. Part A: Using the notation from the previous in-class activity, how would you represent these statistics?
2. Part B: On the following number line, plot and label these statistics using the notation you suggested in the previous question.
   
3. Part C: On the following number line, plot and label the difference p1-p2.
   
4. Where does [latex]\hat{p_{1}} - \hat{p_{2}}[/latex]. lie on the number line in relation to 0? Explain.

Question 5

The survey had 485 respondents who were women and 548 respondents who were men.

1. Part A: How many women who responded said they were vegetarian? Round to the nearest whole number.
2. Part B: How many men who responded said they were vegetarian? Round to the nearest whole number.

Question 6

Go to the DCMP Compare Two Population Proportions tool at https://dcmathpathways.shinyapps.io/2sample_prop/. Under “Enter Data,” select “Number of Successes.” Using Group 1 for the women and Group 2 for the men, input the information from the previous question. Generate a 95% confidence interval for the quantity [latex]p_{1} - p_{2}[/latex]. Sketch and label the interval, and include the quantity [latex]\hat{p_{1}} - \hat{p_{2}}[/latex].

Question 7

7)    For each of the following situations, decide whether the null quantity [latex]p_{1} - p_{2} = 0[/latex] falls within the confidence interval.

1. Part A: Suppose the proportions were those given in Question 4: [latex]p_{1} = \hat{p_{1}}, p_{2} = \hat{p_{2}}[/latex], with the resulting confidence interval from Question 6.
2. Part B: Suppose we had different sample proportions. Suppose now that [latex]\hat{p_{1}} = 0.07[/latex] and [latex]\hat{p_{2}} = 0.02[/latex], with a resulting confidence interval of (0.024, 0.076).
3. Part C: Suppose we had different sample proportions. Suppose now that [latex]\hat{p_{1}} = 0.05[/latex] and [latex]\hat{p_{2}} = 0.057[/latex], with a resulting confidence interval of (–0.034, 0.020).

Question 8

Does the proportion of women who said they were vegetarian have to be greater than the proportion of men who said they were vegetarian in order for [latex]p_{1} - p_{2}[/latex] to fall within the confidence interval?