Answer the following questions with “it increases,” “it decreases,” “it stays th

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.

a. As sample size increases, what happens to the size of the standard error in the z test?

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 tobt increases, what happens to the p value?

d. As tobt increases, what happens to the value of alpha?

e. As power decreases, what happens to the probability of correctly rejecting the null hypothesis?

f. As N increases, what happens to z crit|?

g. As the number of tails in a test increases from one to two, what happens to t crit|?

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

i. If the standard error in a z test increases in value only because the sample size changed, what will happen to the absolute value of Cohen’s d?

j. As degrees of freedom increase, what happens to t crit?

k. As the difference between means decreases and the sample standard deviation increases, what happens to tobt in the single sample t test?

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

m. As tobt increases, what happens to t crit ? n. As |robt| increases, what happens to the likelihood of rejecting H0 that = 0?

o. As N decreases and alpha decreases in value, what happens to r crit?

p. What happens to the width of a confidence interval when you go from having computed a 99% to computing a 95% confidence interval?

Explanation / Answer

a. The size of the standard error decreases because the standard error the sample size-1 as the denominator. so denominator increases and hence standard error decreases.

b.the sample mean also becomes less representatie of the population mean and hence tests or estimation based on the sample mean will be erranious.

c. and d. please give full form of 'tobt'

e.power is defined to be the probability of rejecting the null hypotheses when Ho is false i.e correctly rejecting the null hyp. So as power increases the prob of correctly rejecting the null hypotheses also increases.

f.Zcrit is the upper 0.05 quantile of N(0,1) dist and hence is independent of N. So it remains the same.

g. t_crit increases absolutely. as test become both tailed then typeI error in each taile is halfed so that total typeI error remains same and hence the critical point increases absolutely(as the lower tail is a negative value)

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