Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 46 for a sample of size 21. Assume the population standard deviation is 3.6. 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. Round answers to 2 decimal places where possible.

Answer 1

Solution:

Given:

Sample mean = on average, the reduction in systolic blood pressure =  46

That is:

Sample Size = n = 21

The population standard deviation =  

We have to estimate how much the drug will lower a typical patient's systolic blood pressure using a 90% confidence level.

That is find 90% confidence interval for an average reduction in systolic blood pressure.

Formula:

where

Z_c is z critical value for c = 90% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.90) / 2 = 1.90 / 2 = 0.9500

Look in z table for Area = 0.9500 or its closest area and find corresponding z value.

Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Thus we look for both area and find both z values

Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65

Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645

Thus Z_c = 1.645

Thus

Thus

or we can write in other way: