Which of the following statements are false?
(A) The t-distribution should always be used when n is small.
(B) A test of hypothesis is found to have a p-value of .0682. Then one should conclude H1 if the level of significance is 10% and conclude Ho if the level of significance is 5%.
(C) For a fixed sample size, as confidence decreases so does precision.
(D) The power of a test is the probability of rejecting a null hypothesis when it is false.
Question 6 options:
B and C only
B and D only
A and D only
A and C only
To determine which of the statements are false, we can evaluate each statement individually:
(A) The t-distribution should always be used when n is small.
This statement is false. When n is small, the t-distribution should be used for inference only if the population standard deviation is unknown. If the population standard deviation is known, the standard normal distribution should be used.
(B) A test of hypothesis is found to have a p-value of .0682. Then one should conclude H1 if the level of significance is 10% and conclude Ho if the level of significance is 5%.
This statement is false. The conclusion in a hypothesis test is based on the p-value compared to the chosen level of significance. If the p-value is less than the level of significance, the null hypothesis (Ho) is rejected in favor of the alternative hypothesis (H1). Therefore, if the level of significance is 10% and the p-value is .0682, H1 would be concluded, not Ho.
(C) For a fixed sample size, as confidence decreases, so does precision.
This statement is true. Confidence and precision are inversely related. When confidence decreases, the confidence interval becomes narrower, resulting in decreased precision. Similarly, when confidence increases, the confidence interval becomes wider, resulting in increased precision.
(D) The power of a test is the probability of rejecting a null hypothesis when it is false.
This statement is true. The power of a test is the probability of correctly rejecting the null hypothesis when it is indeed false. It is influenced by factors such as sample size, effect size, and the chosen level of significance.
Based on the evaluations, the false statements are:
(B) A test of hypothesis is found to have a p-value of .0682. Then one should conclude H1 if the level of significance is 10% and conclude Ho if the level of significance is 5%.
(C) For a fixed sample size, as confidence decreases, so does precision.
Therefore, the answer is (B) and (C) only.