Question

P_1

A sample of n = 15 produces a single sample t statistic of t = - 2.12. If the researcher is using a two-tailed test for hypotheses testing, which of the following is the correct statistical decision?

A. The researcher can reject the null hypothesis with α = .05 but not with α = .01.

B. The researcher can reject the null hypothesis with either α = .05 or α = .01.

C. It is impossible to make a decision about H0 without more information.

D. The researcher must fail to reject the null hypothesis with either α = .05 or α = .01.

P_2

If other factors are held constant, what is the effect of decreasing the variability of scores in a sample (i.e., decreasing a sample variance or standard deviation)? Hint: Look at the formulas for the estimated standard error and t-test for a single sample to figure out the answer.

A. It will decrease the estimated standard error and decrease the likelihood of rejecting H₀.

B. It will decrease the estimated standard error and increase the likelihood of rejecting H₀.

C. It will increase the estimated standard error and increase the likelihood of rejecting H₀.

D. It will increase the estimated standard error and decrease the likelihood of rejecting H₀.

P_3

If other factors are held constant, what is the effect of decreasing the sample size? (Hint: Look at the formulas for the estimated standard error and t-test for a single sample to figure out the answer).

A. It will decrease the estimated standard error and decrease the likelihood of rejecting H₀.

B. It will increase the estimated standard error and decrease the likelihood of rejecting H₀.

C. It will decrease the estimated standard error and increase the likelihood of rejecting H₀.

D. It will increase the estimated standard error and increase the likelihood of rejecting H₀.

Answer 1

P1) d.f= N-1=15-1=14 and test statistic= -2.12

Two tailed test.

using t table we have P-Value is .052357.P value >0.05 Therefore it isnot significant.

The researcher must fail to reject the null hypothesis with either α = .05 or α = .01.

P2) t= xbar-\mu/s/\sqrt(n)

s/\sqrt(n) is stanadard error

decreasing s means decreasing standard error which will lead to large value of t test statistic.

It will decrease the estimated standard error and increase the likelihood of rejecting H0.

option B

P3) It will increase the estimated standard error and decrease the likelihood of rejecting H0.

OPTION B