Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 43. 1mmHg (millimeters of mercury) for a sample of size 504 and a sample standard deviation 13. 9mmHg. How much of mmHg will lower for a typical patient's systolic blood pressure after taking the drug? Estimate with a 80% confidence. Preliminary: a. Is it safe to assume that n≤5% of all patients with a systolic blood pressure? No Yes b. Is n≥30 ?

Answer 1

Answer: To estimate how much a typical patient's systolic blood pressure will lower after taking the drug with an 80% confidence level, we can use a confidence interval.

Given data:

Sample size (n) = 504

Sample mean (x) = 43.1 mmHg (reduction in systolic blood pressure)

Sample standard deviation (s) = 13.9 mmHg

The formula for the confidence interval for a population mean with an 80% confidence level is given by:

Confidence Interval = x + Z * (s / √n)

where Z is the critical value corresponding to the confidence level. For an 80% confidence level, the critical value Z is approximately 1.282 (you can find this value from a standard normal distribution table).

Now, let's calculate the confidence interval:

Confidence Interval = 43.1 + 1.282 * (13.9 / √504)

Confidence Interval ≈ 43.1 + 1.282 * (0.619)

Confidence Interval ≈ 43.1 + 0.794

Lower bound of the confidence interval ≈ 43.1 - 0.794 ≈ 42.306 mmHg

Upper bound of the confidence interval ≈ 43.1 + 0.794 ≈ 43.894 mmHg

So, with an 80% confidence level, we can estimate that a typical patient's systolic blood pressure will lower by approximately 42.306 to 43.894 mmHg after taking the drug.

Now, let's answer the preliminary questions:

a. Is it safe to assume that n ≤ 5% of all patients with a systolic blood pressure?

We don't have enough information to determine this based on the given data.

b. Is n ≥ 30?

Yes, n = 504, which is greater than 30.