Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 30.3 for a sample of size 318 and standard deviation 18.8.

Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 80% confidence level).

Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

< μμ <

Answer should be obtained without any preliminary rounding.

Answer 1

Solution:

Given that,

n = 318

= 30.3

s = 18.8  

Note that, Population standard deviation() is unknown..So we use t distribution.

Our aim is to construct 80% confidence interval.   

c = 0.80

= 1- c = 1- 0.80= 0.20

  /2 = 0.10

Also, d.f = n - 1 = 318 - 1 = 317

    =    =  _{0.10 , 317} = 1.284

( use t table or t calculator to find this value..)

The margin of error is given by

E =  /2,d.f. * ( / n)

= 1.284 * (18.8 / 318)

= 1.354

Now , confidence interval for mean() is given by:

( - E ) <   <  ( + E)

(30.3 - 1.354)   <   <  (30.3 + 1.354)

28.9 <   < 31.7