Question

When the following hypotheses are being tested at a level of significance α:

H₀: μ = 500
Hₐ: μ < 500
The null hypothesis will be rejected if the p-value is:

a. Less than α
b. Greater than α
c. Equal to α
d. Less than α/2

Answer 1

The null hypothesis H₀: μ = 500 will be rejected if the p-value is less than the significance level α, indicating substantial evidence against the null hypothesis.

Step-by-step explanation:

When the hypotheses H₀: μ = 500 vs. Hᴇ: μ < 500 are being tested at a level of significance α, the null hypothesis H₀ will be rejected if the p-value is less than α. This is a one-tailed test where the alternative hypothesis suggests that the population mean is less than a specified value. In this context, if we observe a p-value that is less than the chosen significance level α, it provides substantial evidence against the null hypothesis and in favor of the alternative hypothesis.

Therefore, to answer the question, the null hypothesis will be rejected if the p-value is:

• a. Less than α