Please post solution as a picture 13 You are conducting a st

Please post solution as a picture 13. You are conducting a study to see if students do better when they study all at once or in intervals. One group of 12 participants took a test after studying for one hour continuously. The other group of 12 participants took a test after studying for three twenty minute sessions. The first group had a mean score of 75 and a variance of 120. The second group had a mean score of 86 and a variance of 100. a. What is the calculated t value? Are the mean test scores of these two groups significantly different at the .05 level? b. What would the t value be if there were only 6 participants in each group? Would the scores be significant at the .05 level? Rank order the following terms of power

Solution

(a) The test statistic is

t=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(75-86)/sqrt(120/12+100/12)

=-2.57

The degree of freedom =n1+n2-2=12+12-2=22

It is a two-tailied test.

Given a=0.05, the critical values are t(0.025, df=22) =-2.07 or 2.07 (from student t table)

The rejection regions are if t<-2.07 or t>2.07, we reject the null hypothesis.

Since t=-2.57 is less than -2.07, we reject the null hypothesis.

So we can conclude that the mean test scores of these two groups are significantly different

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(b)The test statistic is

t=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(75-86)/sqrt(120/6+100/6)

=-1.82

The degree of freedom =n1+n2-2=6+6-2=10

It is a two-tailied test.

Given a=0.05, the critical values are t(0.025, df=10) =-2.23 or 2.23 (from student t table)

The rejection regions are if t<-2.23 or t>2.23, we reject the null hypothesis.

Since t=-1.82 is between -2.23 and 2.23, we do not reject the null hypothesis.

So we can not conclude that the mean test scores of these two groups are significantly different