Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 83.2 for a sample of size 27 and standard deviation 7.1. 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.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 83.2

sample standard deviation = s = 7.1

sample size = n = 27

Degrees of freedom = df = n - 1 = 27 - 1 = 26

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

t/2,df = 2.056

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

= 2.056 * (7.1 / 27)

Margin of error = E = 2.809

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

- E < < + E

83.2 - 2.809 < < 83.2 + 2.809

80.391 < < 86.009