Question

A researcher is evaluating whether a new intervention affects the average reported anxiety symptoms in a sample of 49 college students. A survey from the previous semester found that the population reported a mean anxiety score of 22 with a standard deviation of 7. The sample completes the same measure of anxiety, with an average score of 20. The researcher sets their alpha level at .05 and performs a two-tailed test to determine whether anxiety increases or decreases after the intervention. Calculate effect size using Cohen’s d. Show all of your calculations for full credit.

Answer 1

Solution :

Given that

Population mean =​​​​​​

Population standard deviation =​​​​​​

Sample mean =​​​​​​

To test whether anxiety increases or decreases after intervention.

We perform two tailed z-test

vs

Test statistic:

​​​​​​

​​​​​​

Critical value at 5% level of significance (From standard normal table)

Decision criteria:

Since,

​​​​​, i. e. 2 > 1.96

Therefore, we reject null hypothesis at 5% level of significance.

Conclusion:

We conclude that anxiety increases or decreases after intervention.

Now, we calculate effect size using cohen's d

Effect size using cohen's d=0.2857