Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 62.4 for a sample of size 1088 and standard deviation 14.5. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 98% confidence level). Enter your answer as a tri-linear inequality accurate to one decimal place

_______ < μ< _________

Answer 1

To estimate the effect of the blood-pressure drug, a 98% confidence interval is constructed using the sample mean of 62.4, standard deviation of 14.5, and the sample size of 1088. The z-score for a 98% confidence level is 2.326, resulting in a margin of error of 1.0231. This yields a trilinear inequality of 61.4 < μ < 63.4 for the reduction in systolic blood pressure.

Step-by-step explanation:

To estimate how much the blood-pressure drug will lower a typical patient's systolic blood pressure with a 98% confidence level, we will construct a confidence interval using the sample mean, standard deviation, and the sample size provided. The formula for the confidence interval is:

mean ± (z-score * (standard deviation / sqrt(sample size)))

The sample mean is 62.4, the standard deviation is 14.5, and the sample size is 1088. The z-score corresponding to a 98% confidence level is approximately 2.326 (which can be found using a z-table or standard normal distribution calculator).

First, calculate the margin of error:

Margin of Error = z-score * (standard deviation / sqrt(sample size))
= 2.326 * (14.5 / sqrt(1088))
= 2.326 * (14.5 / 32.9549)
= 2.326 * 0.4398
= 1.0231

Next, construct the confidence interval:

Lower limit = mean - margin of error
= 62.4 - 1.0231
= 61.3769

Upper limit = mean + margin of error
= 62.4 + 1.0231
= 63.4231

Therefore, the trilinear inequality estimating the reduction in systolic blood pressure is:

61.4 < μ < 63.4