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In a study of 100 new cars, 28 are white. Find p-hat and q-hat, where p-hat is the proportion of new cars that are white.

User Hmallett
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Final answer:

To find p-hat, divide the number of white cars (28) by the total number of cars (100), resulting in p-hat being 0.28. Then subtract p-hat from 1 to get q-hat, which is 0.72. Therefore, 28% of cars are white and 72% are not white in the sample.

Step-by-step explanation:

In the study of 100 new cars where 28 are white, we can calculate π-hat (p-hat) and q-hat. P-hat is the sample proportion of new cars that are white, and q-hat is the proportion of new cars that are not white.

P-hat is calculated as the number of white cars divided by the total number of cars:

P-hat = Number of white cars / Total number of cars
= 28 / 100
= 0.28

Therefore, p-hat is 0.28, which means that 28% of the new cars in the sample are white.

To find q-hat, which is the proportion of new cars that are not white, we subtract p-hat from 1:

q-hat = 1 - p-hat
= 1 - 0.28
= 0.72

Thus, q-hat is 0.72, indicating that 72% of the new cars in the sample are not white.

User Jim Burnell
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