What distinguishes a z-test from a one-sample t-test? A researcher conducted a s

Question

What distinguishes a z-test from a one-sample t-test?

A researcher conducted a study looking at the effect of music education on IQ and got a sample of 40 people to participate in a music education class. The average of the sample’s IQ after participating in the class was 105. We know that the average IQ of the population is 100 with a standard deviation of 15. Which statistical test would be the most appropriate for this study? Why did you come to that conclusion?

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

A t-test is used for testing the mean of one population against a standard or comparing the means of two populations if you do not know the populations' standard deviation and when you have a limited sample (n < 30). If you know the populations' standard deviation, you may use a z-test. ... The samples can be any size

AS in both the cases n>30 we will use z-test

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