Question

Suppose you perform the hypothesis test H₀:μ = 40 versus H₁:μ < 40.

The population variance, σ², is unknown. The sample size is n = 16. Assume the significance level is 0.1.

1) Should you use z or t to find the critical value?
O z
O t

Answer 1

Use a t-distribution to find the critical value for the hypothesis test with an unknown population variance and a sample size of 16, using the significance level of 0.1.

Step-by-step explanation:

You should use a t-distribution to find the critical value when performing the hypothesis test H₀: μ = 40 versus H₁: μ < 40, particularly when the population variance, σ², is unknown and the sample size is small (n = 16). According to the central limit theorem, a normal (z) distribution can be used when the sample size is large, typically n ≥ 30, or when the population variance is known.


However, with a small sample size and an unknown population variance, you need to rely on the t-distribution, where the sample standard deviation is used as an estimate of the population standard deviation. The degrees of freedom in this case would be n - 1, which is 15. Therefore, to perform the hypothesis test, look up the critical value for a t-distribution with 15 degrees of freedom at the significance level of 0.1.