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

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

The differences between a T test and a Z test can be summarised as follows:

1. Both the tests are used for hypothesis testing but Z-test follows a normal distribution whereas T-test follows a T-distribution.
2. T-test is apt when the sample size is small (n < 30) while a Z-test is apt for moderate to large sample sizes (n > 30).
3. Z-test will often require certain assumptions to be met in order to be reliable, making T-test more adaptable.
4. In terms of frequency of use, T-tests are more employed than Z-tests.
5. When the standard deviations are known, Z-tests are preferred over T-tests.

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