Question

1. The National Center for Health Statistics reports that the average systolic blood pressure for males 35-44 years of age has a mean of 122.  The medical director of a large company believes the average systolic blood pressure for male executives 35-44 years of age at his company is different from 122.  He looks at the medical records of 64 randomly selected male executives in this age group and finds that the mean systolic blood pressure in this sample is x̄ = 125.5 and the standard deviation is 24.  The sample does not contain any outliers. You want to create a 99.8% confidence interval for the true average systolic blood pressure of the executives of this company. What is the 99.8% confidence interval?

2. What is the correct interpretation for the interval you created in question 1?

3. For the scenario in question one, are both the assumptions met for the confidence interval to be valid?

   	A.	Yes, both assumptions are met.
   	B.	No, only one assumption is met.
   	C.	No, neither of the assumptions are met.
   	D.	We know one of the assumptions is met. We are unsure about the second assumption, but since the method is robust, it is okay. The confidence interval is still valid.
   	E.	It is impossible to tell.

Answer 1

WE CONSIDER THE NULL HYPOTHESIS (H0):

ALTERNATE HYPOTHESIS H(A) :

SINCE THE CRITICAL VALUE OF t-STATISTIC IN THE  99.8% CONFIDENCE INTERVAL IS [-3.2247 : 3.2247].

THUS USING THIS VALUE IN THE FORMULA TO OBTAIN THE CONFIDENCE INTERVAL.

WHERE, x BAR IS SAMPLE MEAN

MEU NOT IS POPULATION MEAN

S = SAMPLE SD

n = SAMPLE SIZE

WE GET THE CONFIDENCE INTERVAL

[112.3300 , 131.6700].

SINCE WE KNOW THAT HIS ASSUMPTION THAT MEAN SYSTOLIC BLOOD PRESSURE IS DIFFERENT FROM POPULATION MEAN OF 122 IS NOT CORRECT. BECAUSE NULL HYPOTHESIS IS ACCEPTED.

OPTION C IS CORRECT