An independentmeasures research study uses two samples, a total of 23 participants in both samples combined. If the data produce a t statistic of t = 2.10, then which of the following is the correct decision for a twotailed hypothesis test?
Cannot answer without additional information 

Reject the null hypothesis with a = .05 but fail to reject with a = .01. 

Reject the null hypothesis with either a = .05 or a = .01. 

Fail to reject the null hypothesis with either a = .05 or a = .01. 
Solution:
Here we have given that, the test is independent two sample ttest.
n_{1}=n_{2} =23 and the test statistics = 2.10 and the test is two tailed test.
Assuming that the variances are not equal , we use degrees of freedom of unpooled test,so
df = smaller of (n_{1}1)and (n_{2}1) = 22
Then by using T table , with alpha = 0.01 and df = 22,we get critical value tc = 2.819
So decision: Here test statistics t(2.10) < critical value tc,so we fail to reject Ho.
Then with alpha =0.05 and df =22.we get criticla value tc = 2.074
So decision:Here test statistics t(2.10) > critical value tc, so we reject Ho.
Therefore here correct option is 2.Reject the null hypothesis with a = .05 but fail to reject with a = .01.
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