Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 32.3 for a sample of size 22 and standard deviation 13.5. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 99% confidence level). Assume the data is from a normally distributed population.

Answer 1

Experiment is conducted on the effectiveness of blood-pressure drug. According to experimenter on an average reduction in blood pressure is 32.3 and sample size is 22 with a standard deviation of 13.5.

Inorder to obtain the lower patient's blood pressure. We first obtain the confidence interval and the lower value of the confidence interval indicates the patient's lower systolic blood pressure. For this let us consider the null and alternative hypothesis as follows

The confidence interval for the level of significance is given as

The critical value of Z is obtained considering the normal distribution for two tailed confidence interval which is obtained for given level of significance.  

For 99% confidence interval, we have level of significance as (100-99)% =1%=0.01. Therefore for 1% level of significance, the confidence interval is given by

Thus from the above confidence interval we have lower confidence limit as 24.87 and the upper confidence limit as 39.72. Therefore, the drug will typically lower a systolic blood pressure of 24.87.