Question

The mean diastolic blood pressure for a random sample of 60 people was 81 millimeters of mercury. If the standard deviation of individual blood pressure readings is known to be 12 millimeters of mercury, find a 90% confidence interval for the true mean diastolic blood pressure of all people. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. What is the lower limit of the 90% confidence interval? What is the upper limit of the 90% confidence interval? x 5 ?

Answer 1

Here population standard deviation is known so we will use z distribution to find CI

z value for 90% CI is 1.645 as P(-1.645<z<1.645)=0.90

So Margin of Error is $E=z*\frac{\sigma }{\sqrt{n}}=1.645*\frac{12}{\sqrt{60}}=2.548$

Hence CI is $CI=\mu \pm E=81 \pm 2.548=(78.452,83.548)$

Lower 90% CI is 78.452

Upper 90% CI is 83.548