To evaluate the effect of the treatment on intelligence, the researcher should use a z-test when the population standard deviation (σ) is known.

If σ (the population standard deviation) and σ² (the population variance) were unknown, the researcher should use a t-test instead.

Would you like a more detailed explanation of why the z-test and t-test are appropriate in these cases?

Here are 5 related questions to expand your understanding:

1. What is the primary difference between a z-test and a t-test?
2. How does sample size affect the choice between a z-test and a t-test?
3. What is the critical value in hypothesis testing, and how is it determined for a z-test?
4. How would the researcher interpret the p-value in this scenario?
5. What assumptions must be met to perform a t-test?

Tip: When the sample size is large (usually over 30), the t-distribution approaches the z-distribution. Therefore, for large samples, even with an unknown standard deviation, results of the t-test are similar to the z-test.