Confidence Intervals (Mean

Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 79.5 for a sample of size 26 and standard deviation 21.7. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 80% 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

Well, we are assuming that mu and xbar are going to be the same. (a standard assumption as the mean of the sample is an unbiased estimator of the expected value of the population or μ.)

μ = 79.5 σ n = 26 s = 21.7

The upper and lower bounds of the confidence interval are determined by adding and subtracting the calculated margin of error (moe) from mu.

With 26 samples and a sample standard deviation of 21.7 (this is also an assumption as they could be reporting the population standard deviation of the sample. This is a typical assumption) we can calculate the moe.

Using a t distribution we calculate the moe as tcrit _α/2 * s/√n

for alpha = .2 and alpha/2 = .1, and tcrit_α/2 = 1.316, our moe = 1.316*(21.7/√26)

moe = 5.60053

answer = ( 73.899 < μ < 83.101)