MATH SOLVE

4 months ago

Q:
# A researcher conducts a repeated-measures study to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 1.94. The treatment is expected to increase scores and the sample mean shows an increase. Which of the following is the correct decision for a hypothesis test using α = .05.- Reject the null hypothesis with either a one-tailed or a two-tailed test- Fail to reject the null hypothesis with a one-tailed test but reject with two tails- Reject the null hypothesis with a one-tailed test but fail to reject with two tails- Fail to reject the null hypothesis with either a one-tailed or a two-tailed test

Accepted Solution

A:

Answer:Option 3) We reject the null hypothesis with one tail test and accept the null hypothesis with two tail test.Step-by-step explanation:We are given the following information:n = 16[tex]t_{statistic} = 1.94[/tex][tex]\alpha = 0.05[/tex]Now,Right One-tail Test[tex]t_{critical} \text{ at 0.05 level of significance, 15 degree of freedom } = 1.753[/tex][tex]t_{stat} > t_{critical}[/tex]We reject the null hypothesis in this case.Two-tail TestNow, [tex]t_{critical} \text{ at 0.05 level of significance, 9 degree of freedom } = \pm 2.131[/tex] [tex]-2.131 < t_{stat} < 2.131[/tex]We accept the null hypothesis in this case.Option 3) We reject the null hypothesis with one tail test and accept the null hypothesis with two tail test.