In a study of 100 new cars, 29 of them were white. Find $\hat { \mathrm { p } }$ and $\hat { \mathrm { q } }$ where $\hat { \mathrm { p } }$ is the proportion of new cars that is white.
A) $\hat { p } = 0.29 , \hat { q } = 0.29$
B) $\hat { \mathrm { p } } = 0.29 , \hat { \mathrm { q } } = 0.71$
C) $\hat { \mathrm { p } } = 0.71 , \hat { \mathrm { q } } = 0.29$
D) $\hat { \mathrm { p } } = 0.71 , \hat { \mathrm { q } } = 0.71$

Question

Quizplus · Accepted Answer

- The formula for proportion is p = x/n, where x is the number of successes (white cars in this case) and n is the sample size (total number of cars in this case).
- Therefore, $\hat { \mathrm { p } }$ can be calculated as 29/100 = 0.29.
- Since there are only two options (white or not white), we know that q = 1 - p. Therefore, $\hat { \mathrm { q } }$ can be calculated as 1 - 0.29 = 0.71.
- Hence, the correct choice is B.

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