Question

use the results from a survey of a simple random sample of 1199 adults. among the 1199 respondents, 59% rated themselves as above average drivers. we want to test the claim that more than \\( \frac { 11 } { 20 } \\) of adults rate themselves as above average drivers. complete parts (a) through (e).
a. regardless of the conclusion reached from the hypothesis test, is it possible that more than \\( \frac { 11 } { 20 } \\) of adults can be above average drivers?
○ a. no. assuming quality of driving can be quantified, half of all adults must have driving quality less than or equal to the mean.
○ b. yes. assuming quality of driving can be quantified, a distribution that is extremely skewed to the right would be the most promising scenario for more than this proportion of adults to have driving quality that is above the mean.
○ c. yes. assuming quality of driving can be quantified, a distribution that is extremely skewed to the left would be the most promising scenario for more than this proportion of adults to have driving quality that is above the mean.
○ d. no. it is impossible to compare the quality of different adults driving.

Explanation:

• Option A: Incorrect. In a skewed distribution, it's not necessary that half of the data is less than or equal to the mean.
• Option B: Incorrect. A right - skewed distribution has a long right tail. In a right - skewed distribution, the mean is pulled towards the right tail. So, more than half of the data cannot be above the mean in a right - skewed distribution.
• Option C: Correct. In a left - skewed distribution, the mean is pulled towards the left tail. So, it is possible for more than \( \frac{11}{20}=0.55\) of the data (adults' driving quality) to be above the mean.
• Option D: Incorrect. We are assuming that the quality of driving can be quantified for the sake of this problem.

Answer:

C. Yes. Assuming quality of driving can be quantified, a distribution that is extremely skewed to the left would be the most promising scenario for more than this proportion of adults to have driving quality that is above the mean.