A study was conducted of the effects of a special class desi

A study was conducted of the effects of a special class designed to aid students with verbal skills. Each child was given a verbal skills test twice, both before and after completing a 4-week period in the class. Let Y=score on exam at time2-score on exam at time 1. Hence , if the populations mean

Solution

A. Set up the null and alternative hypotheses.

Let mu_d be the mean difference

Null hypothesis: mu_d=0

Alternative hypothesis: mu_d>0

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B. Calculate the test statistic, and indicate whether the p-value was below 0.05, based on the appropriate table.

The test statistic is

t=mean difference/(s/vn)

=(4-0)/(2/sqrt(4))

=4

The degree of freedom =n-1=4-1=3

It is a right-tailed test.

So the p-value= P(t with df=3 >4) =0.0140 (from student t table)

Since the p-value is less than 0.05, we reject the null hypothesis.