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). null hypothesis. d. another memory trick sometimes used is this: \if the p is high, the null will fly.\ given that a hypothesis test never results in a conclusion of proving or supporting a null hypothesis, how is this memory trick misleading? a. this statement seems to suggest that with a high p - value, the null hypothesis has been proven or is supported, but this conclusion cannot be made. b. this statement seems to suggest that with a high p - value, the alternative hypothesis has been rejected, but this conclusion cannot be made. c. this statement seems to suggest that with a high p - value, the alternative hypothesis has been proven or is supported, but this conclusion cannot be made. d. this statement seems to suggest that with a low p - value, the null hypothesis has been proven or is supported, but this conclusion cannot be made.

Explanation:

In hypothesis testing, the null hypothesis ($H_0$) is a statement of no effect or no difference. The P - value is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. A high P - value means that there is not enough evidence to reject the null hypothesis. However, it does not mean that the null hypothesis is proven or supported. The memory trick "If the P is high, the null will fly" seems to imply that a high P - value leads to the acceptance (in the sense of proving or supporting) of the null hypothesis, which is incorrect. Hypothesis testing can only reject or fail to reject the null hypothesis; it cannot prove the null hypothesis.

Answer:

A. This statement seems to suggest that with a high P - value, the null hypothesis has been proven or is supported, but this conclusion cannot be made.