Question

If a hypothesis test were conducted using α = 0.10, for which of the following p-values would the null hypothesis be rejected?

a. 0.065
b. 0.11
c. 0.08
d. 0.15

Answer 1

For a hypothesis test with α = 0.10, the null hypothesis would be rejected for p-values 0.065 and 0.08, as they are less than the chosen significance level.

Step-by-step explanation:

If a hypothesis test were conducted using α = 0.10, the null hypothesis would be rejected for any p-value that is less than the significance level α. In this context, the null hypothesis is rejected if the observed p-value lies in the critical region, which is defined by the significance level. Thus, the null hypothesis is rejected when the p-value is less than 0.10.

• p-value = 0.065: This is less than α = 0.10, so the null hypothesis would be rejected.
• p-value = 0.11: This is greater than α = 0.10, so the null hypothesis would not be rejected.
• p-value = 0.08: This is less than α = 0.10, so the null hypothesis would be rejected.
• p-value = 0.15: This is greater than α = 0.10, so the null hypothesis would not be rejected.

In conclusion, for the given significance level, the null hypothesis would be rejected for p-values 0.065 and 0.08.