Question

The mean diastolic blood pressure for a random sample of 80 people was 99 millimeters of mercury. If the standard deviation of individual blood pressure readings is known to be 11 millimeters of mercury, find a 95% 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. (If necessary, consult a list of formulas.)

What is the lower limit of the 95% confidence interval? What is the upper limit of the 95% confidence interval?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 99

sample standard deviation = s = 11

sample size = n = 80

Degrees of freedom = df = n - 1 = 80-1= 79

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,79 = 1.990

Margin of error = E = t/2,df * (s /n)

= 1.990 * (11 / 80)

E = 2.447

The 95% confidence interval estimate of the population mean is,

- E < < + E

99 - 2.447 < < 99 + 2.447

96.6 < < 101.4

(96.6,101.4)

lower limit of the 95% confidence interval is 96.6

upper limit of the 95% confidence interval is 101.4