Question

If you do a hypothesis test for the mean and you used a t-test instead of a test involving z, and everything else remained the same, your p-value for the t-test would be compared to the p-value for the test involving z.

a. smaller
b. the same
c. larger
d. not predictable

Answer 1

Using a t-test instead of a z-test generally results in a larger p-value, due to the t-distribution's heavier tails compared to the normal distribution. This difference decreases as sample size increases.

Step-by-step explanation:

If you perform a hypothesis test for the mean and you used a t-test instead of a test involving z, and everything else remained the same, your p-value for the t-test would generally be larger compared to the p-value for the test involving z. This is because the t-distribution has heavier tails than the normal distribution, which is used for the z-test, thus resulting in a larger area (and therefore a larger p-value) in the tails of the distribution. This effect is especially noticeable with smaller sample sizes, where the difference between the t-distribution and the normal distribution is most pronounced. As the sample size increases, the t-distribution approaches the normal distribution, and the p-values from the t-test and z-test would become similar.

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