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).
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.
e. common significance levels are 0.01 and 0.05. why would it be unwise to use a significance level with a number like 0.0417?
a. a significance level with more than 2 decimal places has no meaning.
b. using a significance level to more decimal places makes calculations of p - values more difficult.
c. choosing such a specific significance level could give the impression that the significance level was carefully chosen to reach a desired conclusion.
d. choosing a more specific significance level makes it more difficult to reject the null hypothesis.

Explanation:

When conducting hypothesis tests, common significance levels like 0.01 and 0.05 are well - known and widely accepted. A significance level of 0.0417 is an unusually specific value. Choosing such a value might imply that it was deliberately selected to manipulate the result (i.e., to reach a desired conclusion). For example, if the P - value of a test is 0.04, a significance level of 0.05 would lead to rejecting the null hypothesis, while a significance level of 0.0417 might lead to a different conclusion. This gives the impression of bias in the selection of the significance level.

Option A is incorrect because a significance level with more than 2 decimal places can have meaning in some specialized statistical contexts. Option B is incorrect because while more decimal places might make some calculations slightly more complex, this is not the main reason for avoiding such a value. Option D is incorrect because the difficulty of rejecting the null hypothesis is not the key issue with a specific significance level like 0.0417.

Answer:

C. Choosing such a specific significance level could give the impression that the significance level was carefully chosen to reach a desired conclusion.