Question

5. (18 pts) Consider the following situation, and answer each of the following multiple-choice questions. Indicate your answer next to each question in the blank. Possible answers are: A = it increases; B = it decreases; C = it stays the same; D = not enough information to say for sure. No need to restate the question or to justify your answer.

______A. As sample size decreases, what happens to the standard error?   

______B. As a sample becomes less and less representative of the population from which it is drawn, what happens to the value of the sample mean?

______C. As |zobt| increases, what happens to the p value?

______D. As |zobt| increases, what happens to alpha?

______E. As power increases, what happens to the probability of correctly rejecting the null hypothesis?

______F. As N increases, what happens to |zcrit|?

______G. As N increases, what happens to |zobt|?

______H. As the number of tails increases from one to two, what happens to |zcrit|?

______I. As the absolute value of the difference between means decreases, what happens to the absolute value of Cohen’s d?

______J. If the standard error decreases in value only because the sample size changed, what will happen to the absolute value of Cohen’s d?

______K. As N increases, what happens to |tobt|? (Assume the increase in N does not affect the value of s.)  

______L. As degrees of freedom increase, what happens to |tcrit|?

______M. As degrees of freedom increase and alpha decreases in value, what happens to |tcrit|?

______N. As the difference between means increases and the sample standard deviation decreases, what happens to |tobt|?

______O. As degrees of freedom decrease in a single sample t test, what happens to power?

______P. As |tobt| decreases, what happens to |tcrit|?

______Q. As |robt| increases, what happens to the likelihood of rejecting the H0 that ρ = 0?

______R. As N decreases and alpha decreases in value, what happens to |rcrit|?

Answer 1

A) standard error is inversely proportional to the sample size. As sample size decreases, the standard error increases.

Answer is A

B) Answer is C or D

C) As z value increases the p-value decreases.

Answer is B

D) Alpha remains the same. answer is C

E) Answer is A ( power is the probability of correctly rejecting the false null hypothesis)

F) Remains the same Answer is C.

G) test statistic zobt decreases with increase in sample size. answer is B.

H) zcrit increases for two tailed test. Answer is A

I) cohens d is directly proportional to the difference in the means , hence as the absolute value of the difference in the means increases the cohens d value increases. Answer is A.

J) standard error is inversely proportional to cohens d . cohen's d decreases with increase in standard error Answer is B

K) As sample size increases the test statistic tobt decreases. Answer is B.

L) As degrees of freedom increases the critical value of t decreases. Answer is B.

M) tcrit increase . Answer is A.

N) tobt value increases . Answer is A

O) power of the test increases with increase in sample size and viceversa. As degrees of freedom decreases, power of the test decreases. Answer is B.

P) remains same. answer is C.

Q) increases . answer is A

R) rcrit increases with decrease in sample size and increase with decrease in alpha value . Answer is A

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