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.