You are evaluating investing in a cognitive training company. For this reason, y

Question

You are evaluating investing in a cognitive training company. For this reason, you want to determine whether users who complete at least 75% of the recommended daily training for two months show improved levels of reading comprehension and problem solving skills. You select a random sample of new users and get test scores for each participant in the sample. The test score is a composite of reading comprehension and problem solving skills. Two months later, you randomly select 15 users who have completed 75% or more of the recommended training for the last two months and have them take a test similar to the initial test. You are interested in determining whether the average test score before training is different than the average test score after training for this sample. The after-training average is 92.8, which is 2.7 points higher than the before- training average. The sample standard deviations of the differences is 1.2. You use a significance level of 0.10, and you can assume that the differences are normally distributed in the population. The table t-value for this test is_ oths ltestteiatio ation. stribidard traininit 1.761 0 1.746 1.753 O 1.345 1.339

Explanation / Answer

1)

Ans) 1.345

If we look at the t table for one tail 10% and degree of freedom 15-1 i.e 14 we get the value 1.345

2)

p=0.15

1-p=0.85

SE= sqrt ( 0.15*0.85*(1/400+1/400)

      = sqrt(0.1275/200)

     = sqrt(0.0006375)

     = 0.02524

Ans ) 0.0459

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