The 2014 Public Health Survey sampled 2,035 people and found an average systolic

Question

The 2014 Public Health Survey sampled 2,035 people and found an average systolic blood pressure reading (top #) of 134.65, a median of 119.56 and a standard deviation of 12.52.

a. What is the point estimate of the population mean?

b. Find the standard error of the sample mean.

c. Compute the 95% confidence interval of the population mean and interpret it. You should demonstrate an interval with a lower-bound value and an upper-bound value, where the #’s enclose the population parameter

d. Is it plausible that the population mean could be equal to 136? Explain.Observe whether the interval encloses the specified value of the parameter 136

Explanation / Answer

a. Point estimate of population mean is sample mean=134.65

b. As n=2,035 which is sufficient large so as per central limit theorem sample mean is normally distributed with mean =xbar and sd=sd/sqrt(n)

So here sd=12.52/sqrt(2035)=0.2775

c. Here z=1.96

So Margin of Error=z*sd/sqrt(n)=1.96*0.2775=0.5439

Hence CI=mean+/-E=134.65+/-0.5439=(134.1061,135.1939)

d. As 136 is not in the range it is not plausible that the population mean could be equal to 136.

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