Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 44 for a sample of size 18 and standard deviation 13.

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

Give your answers to one decimal place and provide the point estimate with its margin of error.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 44

sample standard deviation = s = 13

sample size = n = 18

Degrees of freedom = df = n - 1 = 18 - 1 = 17

At 80% confidence level

= 1 - 80%

=1 - 0.80

= 0.20

t/,df = t0.20,17 = 0.863

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

= 0.863 * ( 13/ 18 )

Margin of error = E = 2.6

The 80% lower confidence interval estimate of the population mean is,

- E  

= 44 - 2.6 = 41.4

lower limit = 41.4