This survey randomly samples households across the US and asks questions on demographics, income, education, political affiliation, voting history, and perspectives on current social issues. The 2021 data (from form A) on race and highest level of educational attainment is presented below:

| Race | Less than High School | High School | Associate/Junior College | Bachelor's or Graduate | Total |
|-------|------------------------|-------------|--------------------------|-----------------------|-------|
| Black | 15 | 70 | 19 | 61 | 165 |
| White | 55 | 388 | 101 | 485 | 1029 |
| Other | 15 | 48 | 8 | 62 | 133 |
| Total | 85 | 506 | 128 | 608 | 1327 |

Present your answers in decimal form to 2 decimal places. (30 points, 5 for each part)

a. Is this analysis an observational study or a designed experiment? Why?

b. If a respondent is chosen at random, find the probability that the respondent's highest degree is a Bachelor's or Graduate degree.

c. If a respondent is chosen at random, find the probability that the respondent's highest degree is a Bachelor's or Graduate degree or the respondent is Black.

d. If a respondent is chosen at random, find the probability that the respondent's highest degree is a Bachelor's or Graduate degree given that the respondent is Black.

e. If a respondent is chosen at random, find the probability that the respondent's highest degree is a Bachelor's or Graduate degree given that the respondent is White.

f. Does attainment of a Bachelor's or Graduate degree seem to be related to the respondent’s race? Explain your answer in one to three well-formulated sentences that refer back to your calculations above. Please use scrap paper to develop your sentences. Submit only your final sentences.

The analysis presented in the given table is an observational study. The probability that a respondent's highest degree is a Bachelor's or Graduate degree is 50.6%.

There is a higher probability that a respondent with a Bachelor's or Graduate degree is Black (32.7%) compared to White (50.6%). The attainment of a Bachelor's or Graduate degree appears to be related to the respondent's race.

a. This analysis is an observational study, as the data is collected from existing sources and analyzed without any manipulation or random assignment of participants.

b. The probability that a respondent's highest degree is a Bachelor's or Graduate degree is 50.6% (85/170).

c. The probability that a respondent's highest degree is a Bachelor's or Graduate degree or the respondent is Black is 32.7% (388+19+61+165)/(170*55) = 0.327 or approximately 32.7%.

d. The probability that a respondent's highest degree is a Bachelor's or Graduate degree given that the respondent is Black is 0.496 or approximately 49.6%.

e. The probability that a respondent's highest degree is a Bachelor's or Graduate degree given that the respondent is White is 50.6% (101+101)/(388+101) = 0.506 or approximately 50.6%.

f. Attainment of a Bachelor's or Graduate degree seems to be related to the respondent’s race, as there is a higher probability that a respondent with a Bachelor's or Graduate degree is Black compared to White.

Hence, There is a higher probability that a respondent with a Bachelor's or Graduate degree is Black (32.7%) compared to White (50.6%). The attainment of a Bachelor's or Graduate degree appears to be related to the respondent's race.

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