Chapter 9.2, Problem 9.35E

a)

To determine

To explain result.

Explanation of Solution

Given:

Austin says that a result that is significant at the a = 0.05 level must also be significant at the a = 0.01 level.

First need to know decision rule:

If the p-value =a then reject null hypothesis and result is significant

Therefore, it is not necessary that the result that is significant at the a = 0.05 level must also be significant at the a = 0.01 level.

For example, if p-value = 0.0345

If a = 0.05 then p = 0.0345<0.05, the result is significant.

If a = 0.01 then p = 0.0345>0.01, the result is insignificant.

Hence, given statement is incorrect.

b)

To determine

To explain result.

Explanation of Solution

Given:

Asked to explain the meaning of "statistically significant at the a = 0.05 level," Carla says: "This means that the probability that the null hypothesis is true is less than 0.05

First need to know decision rule:

If the p-value =a then reject null hypothesis and result is significant

P-value is capable to determine the probability that the null hypothesis is false. Therefore, the statistically significant at the a = 0.05 level. That means that the probability that the null hypothesis is false is less than 0.05. Hence, given statement is incorrect.