Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 26.8 for a sample of size 29 and standard deviation 6.6. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level). Assume the data is from a normally distributed population.

Enter your answer as a tri-linear inequality accurate to three decimal places.

____ < μ < _____

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 26.8

sample standard deviation = s = 6.6

sample size = n = 29

Degrees of freedom = df = n - 1 = 29 - 1 = 28

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,28 = 2.048

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

= 2.048 * (6.6 / 29)

Margin of error = E = 2.510

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

- E < < + E

26.8 - 2.510 < < 26.8 + 2.510

24.290 < < 29.310