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

With 98% confidence, the drug is estimated to lower a typical patient's systolic blood pressure by between 61.4 and 63.4 mm Hg.

Step-by-step explanation:

To estimate how much the drug will lower a typical patient's systolic blood pressure at a 98% confidence level, we can use the formula for the confidence interval for the mean μ of the normally distributed data. The formula is given by μ = μ ± Z*(σ/√n), where μ is the sample mean, Z* is the Z-value corresponding to the confidence level, σ is the standard deviation, and n is the sample size.

Here, the sample mean (μ) is 62.4, the standard deviation (σ) is 14.5, and the sample size (n) is 1088. To find the Z-value for a 98% confidence interval, we refer to the Z-table for the value corresponding to 99% (since 98% confidence means 1% is on each side of the distribution) which gives us approximately 2.33.

Now, calculate the margin of error (E):

E = Z*(σ/√n) = 2.33 * (14.5/√1088) ≈ 1.03.

Constructing the confidence interval gives us:

61.4 < μ < 63.4

Therefore, with 98% confidence, we can say that the drug will lower a typical patient's systolic blood pressure by between 61.4 and 63.4 millimeters of mercury (mm Hg).