Answer the following questions with \"it increases, \" \"it decreases, \" \"it s

Question

Answer the following questions with "it increases, " "it decreases, " "it stays the same, " or "not enough information to answer." Assume any factors in the situation not mentioned in the problem remain the same. In your write-up, just list the sub-question letter and your answer - 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 |Z_obc| increases, what happens to the p value? D. As |Z_obt| 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 |Z_cirt|? G. As N increases, what happens to |Z_obt|? H. As the number of tails increases from one to two, what happens to |Z_cirt|? 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 si ze changed, what will happen to the absolute value of Cohen's d? K. As N increases, what happens to |t_obt|? (Assume the increase in N does not affect the value of s.) L. As degrees of freedom increase, what happens to |t_cirt|? M. As degrees of freedom increase and alpha decreases in value, what happens to |t_cirt|? N. As the difference between means increases and the sample standard deviation decreases, what happens to |t_obt|? O. As degrees of freedom decrease in a single sample t test, what happens to power? P. As |t_obt| decreases, what happens to |t_cirt|? Q. As |r_obt| increases, what happens to the likelihood of rejecting the H_0 that rho = 0? R. As N decreases and alpha decreases in value, what happens to |r_obt|?

Explanation / Answer

a) Since standard error is inversely proportional to the sample size (s.e. = sigma / sqrt(n) , n : sample size), so as sample size increases, standard error decreases.

b) In this case sample mean will not be a good estimate of the population mean.

c) The p-value decreases. As p-value = P(Z>Zobs) + P(Z<Zobs)

d) Zobs is independent of alpha. So alpha will not be affected by Zobs.

e) Since power = P(Rej H0 | H1) , so as power increases, the probability of correctly rejecting null hypothesis increases.

f) Zcric is independent of N. So it will remain unchanged.

g) As N i.e. sample size increases Zobs also increases.

h) In this case Zcric will take two values with opposite signs. But since the tails have changed, |Zcric| will increase.

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