Find the t-values that form the boundaries of the critical region for a two-tail

Question

Find the t-values that form the boundaries of the critical region for a two-tailed test with x=.05 for each of the following sample size (N) values.

N = 12 (1 point)

N = 24 (1 point)

N = 36 (1 point)

Based on the answers for (a) to (c) above, what can you glean about the relationship between sample size and the critical value? (1 point)

If you have the same t statistic but different sample sizes in two studies, is it more or less likely to have a significant result with the larger sample size? (1 point)

Explanation / Answer

Here, level of significance=x=0.05 , x/2=0.05/2=0.025

(a) Here, N=sample size=12

Critical value corresponding to this sample size is given by ,

tN-1,x/2=t11,0.025=2.200985 ......From t-distribution table

(b)Here, N=sample size=24

Critical value corresponding to this sample size is given by ,

tN-1,x/2=t23,0.025=2.068658 ......From t-distribution table

(c)Here, N=sample size=36

Critical value corresponding to this sample size is given by ,

tN-1,x/2=t35,0.025=2.030108 ......From t-distribution table

Based on the answers for (a) to (c) above, as sample size increases , the critical value decreases.

Also, if you have the same t statistic but different sample sizes in two studies, it is more likely to have a significant result with the larger sample size  because as sample size increases , the area under the acceptance region decreases & which result in increase of sensitivity of test.

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