A researcher conducts a related-sample study to evaluate two treatments with n = 16 participants and obtains a t statistic of t = 1.94. The treatment 2 is expected to have a greater sample mean than the treatment 1. What is the correct decision for a hypothesis test using α = .05?

Not enough statistical evidence to prove that treatment 2 sample mean u2 is less than treatment 1 sample mean u1. So the claim may be supported.

Step-by-step explanation:

Solution:-

- The sample size of two treatments, n = 16

- The mean of sample treatment 1, u1

- The mean of sample treatment 2 , u2

- The significance level, α = .05

- State the hypothesis:

                      Null hypothesis : u2 - u1 > 0

                      Alternate hypothesis : u2 - u1 ≤ 0

- The rejection region of the T- critical for lower tailed test.

                      significance level, α = .05

                      degree of freedom v = n - 1 = 16 - 1 = 15

                      T-critical =  - 1.75

- The T-test value is compared with T-critical:

                      T-test = 1.94

                      T- critical = -1.75

                      T-test > T-critical  .. ( Null not rejected )

- Not enough statistical evidence to prove that treatment 2 sample mean u2 is less than treatment 1 sample mean u1. So the claim maybe supported.

step-by-step explanation: