Question

The mean salary for nurses in North Carolina is $66,440. A local hospital claims their salaries are not different than the mean for North Carolina. The hospital hires a statistician and the statistician provides the following summary.

H₀ µ = 66,400 (claim)
H₁ µ ≠ 66,400
P-value = 0.114

Using a significance level of 0.05, choose the correct decision and interpretation.

		Fail to reject the null hypothesis. At a significance level of 0.05, there is not enough information to support the hospitals’ claim that their nurses’ salaries are not different from the mean salary for nurses in North Carolina.
		Reject the null hypothesis. At a significance level of 0.05, there is enough information to reject the hospitals’ claim that their nurses’ salaries are not different from the mean salary for nurses in North Carolina.
		Fail to reject the null hypothesis. At a significance level of 0.05, there is enough information to reject the hospitals’ claim that their nurses’ salaries are not different from the mean salary for nurses in North Carolina.
		Fail to reject the null hypothesis. At a significance level of 0.05, there is not enough information to reject the hospitals’ claim that their nurses’ salaries are not different from the mean salary for nurses in North Carolina.
		Reject the null hypothesis. At a significance level of 0.05, there is not enough information to reject the hospitals’ claim that their nurses’ salaries are not different from the mean salary for nurses in North Carolina.
		Reject the null hypothesis. At a significance level of 0.05, there is not enough information to support the hospitals’ claim that their nurses’ salaries are not different from the mean salary for nurses in North Carolina.

Answer 1

Solution:

Given data

Null hypothesis H0: µ = 66,400 (claim)

Alternative hypothesis H1: µ ≠ 66,400

This is "two - tailed" test

P- Value = 0.114

Significance level () = 0.05

Decision:

P- Value >

0.114 > 0.05

So we fail to reject the null hypothesis(H0) because the P- Value is greater than significance level.

Conclusion:

Fail to reject the null hypothesis. At a significance level of 0.05, there is not enough information to support the hospitals’ claim that their nurses’ salaries are different from the mean salary for nurses in North Carolina.

Therefore the "Option - A" is the correct answer.