Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 54.7 for a sample of size 22 and standard deviation 17.5. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 90% confidence level). Assume the data is from a normally distributed population. Enter your answer as a tri-linear inequality accurate to three decimal places

answer ____  < μμ < ____ answer

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 54.7

sample standard deviation = s = 17.5

sample size = n = 22

Degrees of freedom = df = n - 1 = 22 - 1 = 21

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,21 = 1.721

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

= 1.721 * (17.5 / 22)

= 6.421

The 90% confidence interval estimate of the population mean is,

- E < < + E

54.7 - 6.421 < < 54.7 + 6.421

48.297 < < 61.121