Question 1

Use the graphic to answer the following questions.

1. Part A: What percentage of all adults surveyed said that their financial situations were about the same as one year earlier?
2. Part B: How would you write this proportion as a decimal?
3. Part C: How many adults surveyed said their financial situations were about the  same as one year earlier?
4. Part D: Is your answer to Part C a reasonable answer? If not, describe how you  would adjust your response to Part C in order to find the number of adults surveyed who said that their financial situations were about the same as one  year earlier.
5. Part E: Use a fraction to express the proportion of adults surveyed who said that  their financial situations were about the same as one year earlier.

Question 2

Using information from the methodology of the survey,^[2] we find that about 2,279  middle-income respondents said that their financial situations were about the same  as one year earlier and about 982 upper-income respondents said the same.

1. Part A: Does this mean that people in the middle-income category are more likely to  have a financial situation that didn’t changed much in the last year?
2. Part B: It turns out that there were about 4,650 middle-income respondents and 1,963 upper-income respondents. What proportion of each group reported  financial situations that were about the same as a year earlier?

Question 3

What percentage of adults surveyed reported financial situations that were not about  the same as one year earlier? Describe at least two ways to find this.

Question 4

Would you expect the proportion of U.S. adults who said their financial situations were better than they were one year earlier to be higher among lower-income adults or upper-income adults? Explain.

Question 5

How does the data compare with your answer to Question 4?

Question 6

Let [latex]p_{L}[/latex] represent the true proportion of all U.S. lower-income adults who said their financial situations were better than they were one year earlier, and let [latex]P_{U}[/latex] represent the true proportion of all U.S. upper-income adults who said their financial situations were better than they were one year earlier.

1. Part A: Write an inequality that relates these two quantities.
2. Part B: Do you expect the quantity [latex]p_{L} -  P_{U}[/latex] to be positive or negative? Explain.
3. Part C: Express your answer to Part B using an inequality.
4. Part D: Do you expect the quantity [latex]p_{L} -  P_{U}[/latex] to be positive or negative? Explain.
5. Part E: Express your answer to Part D using an inequality.

Question 7

Let [latex]\hat{p_{L}}[/latex] represent the sample proportion (written as a decimal) of lower-income respondents who said their financial situations were better than they were one year earlier, and let [latex]\hat{p_{U}}[/latex] represent the sample proportion (written as a decimal) of upper-income respondents who said their financial situations were better than they were one year earlier.

Label [latex]\hat{p_{L}}[/latex] and [latex]\hat{p_{U}}[/latex] on the following number line. Use the number line to explain whether [latex]\hat{p_{U}} - \hat{p_{L}}[/latex] is positive or negative.

Hint: You can find the values of [latex]\hat{p_{L}}[/latex] and [latex]\hat{p_{U}}[/latex] in the graphic containing information from the article.

Question 8

On its own, does your answer to Question 5 provide enough evidence to support your answer to Question 4?