Question

The mean diastolic blood pressure for a random sample of 70 people was 90 millimeters of mercury. If the standard deviation of individual blood pressure readings is known to be 11 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 = = 90

Population standard deviation =    = 11
Sample size = n =70

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2    * ( /n)

= 1.645 * (11 /  70 )

=2.2
At 90% confidence interval estimate of the population mean
is,

- E < < + E

90 -2.2   <   < 90 + 2.2  

87.8 <   < 92.2

( 87.8 <, 92.2)