Question

1. The P-value of a test of the null hypothesis is

a. the probability the null hypothesis is true.

b. the probability the null hypothesis is false.

c. the probability, assuming the null hypothesis is false, that the test statistic will take a value at least as extreme as that actually observed.

d. the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed.

2. The P-value of a test of hypotheses is P = 0.0591. The conditions for the test are met. Based on this P-value,

a. you reject H0 at significance level 0.10, but not at significance level 0.05.

b. you reject H0 at significance level 0.05, but not at significance level 0.01.

c. H0 is proved at significance level 0.01.

d. you fail to reject H0 at significance level 0.10.

3. Which of the following will increase the value of the power in a statistical test of hypotheses?

a. Increase the Type II error probability.

b. Reject the null hypothesis only if the P-value is smaller than the level of significance.

c. Increase the sample size.

d. All of the above

4. A 99% confidence interval for the mean  of a population is computed from a random sample and found to be 6 ± 3. We may conclude that

a. if we took many, many additional random samples, and from each computed a 99% confidence interval for , approximately 99% of these intervals would contain .

b. the true mean is 6 and the true margin of error is 3, both with 99% probability

c. there is a 99% probability that  is between 3 and 9.

d. All of the above.

PLEASE ANSWER THESE AND EXPLAIN

Answer 1