Determine whether to reject or fail to reject H_{0} at the level of significance of a) α = 0.06 and b) α = 0.09.

H_{0}: µ = 110, H_{a}: µ ≠ 110, and P = 0.0769.

**Solution:-**

a) Do you reject or fail to reject H_{0} at the 0.06 level of significance?

When you assume the null hypothesis is true, a P-value of a hypothesis test is the probability of obtaining a sample with a value as extreme or more extreme that the one determine from the sample data.

If the P-value is less than or equal to the level significance, than reject H_{0}. If the P-value is greater than the value of significance, than fail to reject H_{0}.

Fail to reject H_{0} because 0.0769 > 0.06.

b) Do you reject or fail to reject H_{0} at the 0.09 level of significance?

If the P-value is less than or equal to the level of significance, than reject H_{0}. If the P-value is greater than the level of significance, than fail to reject H_{0}.

Reject H_{0} because 0.0769 < 0.09.