confidenc elevel

Question

An experimenter finds that, on average, the reduction in systolic blood pressure is 16.9 for a sample of size 547 and standard deviation 6.4.

Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 98% confidence level).

Answer 1

To estimate how much the drug will lower a typical patient's systolic blood pressure with a 98% confidence level, we can use the formula for the confidence interval of a population mean:

Confidence Interval = X̄ ± Z * (σ / √n)

Where:

X̄ is the sample mean (average reduction in systolic blood pressure),

Z is the Z-value corresponding to the desired confidence level (98% confidence level corresponds to a Z-value of approximately 2.33),

σ is the population standard deviation (6.4),

n is the sample size (547).

Substituting the values into the formula:

Confidence Interval = 16.9 ± 2.33 * (6.4 / √547)

Calculating the value inside the parentheses:

6.4 / √547 ≈ 0.273

Calculating the confidence interval:

Confidence Interval ≈ 16.9 ± 2.33 * 0.273

Confidence Interval ≈ 16.9 ± 0.636

Thus, the 98% confidence interval estimate for how much the drug will lower a typical patient's systolic blood pressure is approximately 16.264 to 17.536.

Answer 2

Here is Dr. C's step by step solution to this question. I hope this helps! If you have any questions, let me know. :)