# A researcher is conducting a study to examine the effects of cognitive behavior therapy for the treatment of social anxiety in a sample of 16 participants.

A researcher is conducting a study to examine the effects of cognitive behavior therapy for the treatment of social anxiety in a sample of 16 participants. He measures the social anxiety scores of participants before the tratment and then again after treatment and the resulting data is as follows:
$n=16,{M}_{0}=5,s=4$
a) What type of design is this study (single-sample, independent measures, repeated measures)
b)State the null and alternate hypotheses
c) Using an , identify the critical values of t for a 2-tailed test.

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Step 1
Experiment is conducted to study effect of cognitive behavior therapy for treatment of social anxiety.
a) This would be repeated measure study, since observations are noted for study before performing the experiment and after the experiment.
Data is
$n=16,{M}_{0}=5,s=4$
Step 2
b) Hypotheses can be constructed as:
${H}_{0}$: There is no effect of cognitive behavior therapy for the treatment of social anxiety.
${H}_{1}$: There is effect of cognitive behavior therapy for the treatment of social anxiety.
c) Significance level $\left(\alpha \right)=0.05$
This data follows t-distribution with 15 degrees of freedom.
Critical value, ${t}_{\left(n-1\right),\frac{\alpha }{2}}={t}_{\left(16-1\right),\frac{0.05}{2}}=2.1314$ (calculated from t-table)