Question

Assuming all other things are equal, are you more likely to reject the null when conducting a one-sample z-test or a one-sample t-test?

a) A − test and t-test are interchangeable.
b) Azetest
c) A t-test
d) There is not enough informution to answer this question.

Answer 1

You are more likely to reject the null hypothesis with a one-sample z-test compared to a one-sample t-test, since the z-distribution is narrower and relies on a known population standard deviation.

Step-by-step explanation:

Assuming all other things are equal, one is more likely to reject the null hypothesis when conducting a one-sample z-test compared to a one-sample t-test. The reason is that a z-test uses the population standard deviation, which provides a more precise estimate of the population parameters when known, and the z-distribution is narrower than the t-distribution, leading to a higher likelihood of rejecting the null for the same sample statistic. However, the z-test is only appropriate when you have a large sample size or the population standard deviation is known. Conversely, a t-test is used when the sample size is smaller and the population standard deviation is unknown, making the test statistic more susceptible to variability, leading to a wider t-distribution and a less likely rejection of the null hypothesis for the same level of significance.