An independent-measures research study uses two samples, each with n= 10 participants. if the data produce a t statistic of t = 2.095, which of the following is the correct decision for a two-tailed hypothesis test?
reject the null hypothesis with α = .05 but fail to reject with α = .01
fail to reject the null hypothesis with either α = .05 or α = .01
reject the null hypothesis with either α = .05 or α = .01
cannot answer without additional informations

The correct option is (B) Fail to reject the null hypothesis with either α = .05 or α = .01

Step-by-step explanation:

Consider the provided information.

The size of sample 1 = n1 = 10

The size of sample 2 = n2 = 10

It is given that the test statistic is: t = 2.095

For  α = 0.05

ndf = n1 + n2 - 2

Substitute the respective values in the above formula.

ndf = 10 + 10 - 2 = 18

Two Tailed Test:

From the table, critical value of t = 2.1009

But the calculated value of t = 2.095 which is less than critical value of t = 2.1009, Fail to reject .  

For  α = 0.01

From the table, critical value of t = 2.8784

But the calculated value of t = 2.095 which is less than critical value of t = 2.8784, Fail to reject .  

Hence, the correct option is (B) Fail to reject the null hypothesis with either α = .05 or α = .01