A researcher wanted to investigate the effect of CBT on anxiety levels. To do so

Question

A researcher wanted to investigate the effect of CBT on anxiety levels. To do so, she recruits 100 people with anxiety and has them participate in an 8-week CBT treatment program. At the end, the average anxiety for the sample was 59 (out of 100) with an estimated population variance of 47. We know that the average anxiety score in a population of people who have an anxiety disorder is 78, but we don’t know the variability of the population. Which statistical test would be the most appropriate for this study? Why did you come to that conclusion?

Explanation / Answer

Hypothesis test for single mean.

since we are hypothesising about population mean

Null hypothesis

Ho:mu=78

H1:mu not=78

alpha=0.05

z=sample mean-population mean/sd/sqrt(n)

=59-78/sqrt(47/100)

=-19/0.685565

=-27.7143

p value<0.0001

p<0.05

Reject Null Hypothesis

There is suffiicent statistical evidence at 5% level of sugnificance to conclude that there is an effect of CBT on anxiety levels

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