Question

he effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 43 for a sample of size 10 and standard deviation 18. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level). Give your answers to one decimal place and provide the point estimate with its margin of error.

___ ±____

Answer 1

We are given sample average reduction in systolic blood pressure is 43 and sample standard deviation is 18

= 43 and  s  = 18 and n is sample size = 10

The best point estimate of population mean is sample mean

Thererore point estimate for reduction in systolic blood pressure is 43.

Margin of error E = s is sample standard deviation and n is sample size.

t is critical value follows t distribution with degrees of freedom (d.f ) = n-1

(here population standard deviation is unknown therefore we need to use t distribution)

n = 10 , therefore d.f = n - 1 = 10- 1 = 9

We are given confidence level = 95% or 0.95

Therefore to find t we need to look for d.f = 9 and across confidence level 0.95

We got t = 2.262 from t distribution table.

Margin of error E =   = 12.8755

Therefore point estimate = 43 and margin of error = 12.8755

Confidence interval is given by ,

E   

Fill in the blanks would be 43 12.9 ---- ( rounded to one decimal places )

and 95% confidence interval would be ( 30.1 , 55.9 )