13 You are conducting a study to see if students do better w

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?

Solution

There are two groups

n1=n2 =12

x1 bar = 75

x2 bar = 86

var (x1) = 120

var(x2) = 100

H0: mu1 = mu2

Ha: mu1>mu2

Right tailed hypothesis test for testing 2 means.

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X1 bar - x2 bar = - 11

95% CI of difference:
-99.3798 <-11< 77.38

std dev = 208.15 and se = 45.092

t statisitc =-0.244

p value =0.40326

As p value >0.05, we accept null hypothesis.

That is there is no statistical evidence to prove that first group has better performance than ii.

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Let n1 = n2 =6

sd=198.46; se=63.77

t statistic = -0.172

p value = 0.43218

Same decision as above as p value > alpha.