Question

the effectiveness of a blood - pressure drug is being investigated. an experimenter finds that, on average, the reduction in systolic blood pressure is 72.8 for a sample of size 759 and standard deviation 11.2. estimate how much the drug will lower a typical patients systolic blood pressure (using a 80% confidence level). enter your answer as a tri - linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place). <\mu< answer should be obtained without any preliminary rounding. question help: video post to forum

Explanation:

Step1: Find the critical value

Since the confidence level is \(80\%\), the significance level \(\alpha = 1 - 0.80=0.20\), and \(\alpha/2 = 0.10\).
For a large - sample (\(n = 759\)) from the standard normal distribution \(Z_{\alpha/2}=Z_{0.10}\approx1.28\) (using standard normal distribution tables or a calculator).

Step2: Calculate the margin of error

The formula for the margin of error \(E\) is \(E = Z_{\alpha/2}\frac{s}{\sqrt{n}}\), where \(s = 11.2\) and \(n = 759\).

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Step3: Calculate the confidence interval

The sample mean \(\bar{x}=72.8\).
The confidence interval for the population mean \(\mu\) is \(\bar{x}-E<\mu<\bar{x} + E\).
Substitute \(\bar{x}=72.8\) and \(E = 0.52\) into the formula:
\(72.8- 0.52<\mu<72.8 + 0.52\)

Answer:

\(72.3<\mu<73.3\)