Question

You conduct a two­sided hypothesis test for the difference between two means based on a matched pairs comparison between two data sets of size 15, and get a t value of 2.55. Which of the following is true for this test?a. This finding is significant at neither the .05 nor the .01 levels.b. This finding is significant at the .05 level but not at the .01 level.c. This finding is significant at the .01 level but not at the .05 level.d. This finding is significant at both the .05 and the .01 levels.e. You need to know the sample standard deviations in order to answer this question

Answer 1

b. This finding is significant at the .05 level but not at the .01 level.c. This finding is significant at the .01 level but not at the .05 level

Explanation:

given that you conduct a two­sided hypothesis test for the difference between two means based on a matched pairs comparison between two data sets of size 15, and get a t value of 2.55.

Sample size = 15

Hence degrees of freedom= 15-1 =14

t statistic = 2.55

Let us find p value for this test statistic two tailed.

p value =0.023117

This p value <0.05. Hence at 5% significance level we reject H0

But for 1% level, we find p is greater than1% so at 1% level we accept H0.

b. This finding is significant at the .05 level but not at the .01 level.c. This finding is significant at the .01 level but not at the .05 level