Question

Company executives’ blood pressure

The National Center for Health Statistics reports that the systolic blood pressure for males 35 to 44 years of age has mean 128. The medical director of a large company looks at the medical records of 72 executives in this age group and finds that the mean systolic blood pressure in this sample is = 126.07. Is this evidence that the company’s executives have a different mean blood pressure from the general population? (Suppose we know that executives’ blood pressures follow a Normal distribution with standard deviation σ= 15.)

1) (4 points)Write down null and alternative hypotheses, both in symbols and in words.

2) (4 points)Calculate the appropriate Test Statistic.

3) (4 points)Find the P-value.

4) (3 points)Suppose the level of significance is 10%, draw your conclusions.

5) (6 points)Construct a confidence interval to re-answer the question “Is the observed mean blood pressures, 126.07, of executives significantly different from the national meanμ₀ = 128 at the 10% significance level? [Hint: Consider a confidence level of 90% when you construct the confidence interval. Think about why.]

Answer 1

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


Z = -1.0918

Test Criteria :-
Reject null hypothesis if


Result :- Fail to reject null hypothesis

P value = 2 * P ( Z < -1.09 ) = 0.2749

Decision based on P value
P value = 2 * P ( Z < -1.09 ) = 0.2749
Reject null hypothesis if P value < level of significance
P - value = 0.2749 > 0.10 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

Confidence Interval :-



Lower Limit =
Lower Limit = 123.1623
Upper Limit =
Upper Limit = 128.9777
90% Confidence interval is ( 123.1623 , 128.9777 )

Since   lies in the interval ( 123.1623 , 128.9777 ) , hence we fail to reject null hypothesis

There is insufficient evidence to support the claim that significantly different from the national mean μ₀ = 128 at the 10% significance level.