Question

The mean diastolic blood pressure for a random sample of 100 people was 81 millimeters of mercury. If the standard deviation of individual blood pressure readings is known to be 10 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?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 81

Population standard deviation =    = 10

Sample size = n = 100

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

Margin of error = E = Z/2 * ( /n)

= 1.645 * ( 10 /  100 )

= 1.645

At 90% confidence interval estimate of the population mean is,

- E < < + E

81 - 1.645 <   < 81 + 1.645

79.355 <   < 82.645

79.4  <   < 82.6

( 79.4 , 82.6 )

The lower limit of the 90% confidence interval = 79.4

The upper limit of the 90% confidence interval = 82.6