The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 70.2 for a sample of size 25 and standard deviation 17.7. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 98% confidence level). Assume the data is from a normally distributed population.
Enter your answer as a tri-linear inequality accurate to three
decimal places.
__________< μ < ______
Solution :
Given that,
sample size = n = 25
Degrees of freedom = df = n - 1 = 25 - 1 = 24
t_{ /2,df} = 2.492
Margin of error = E = t_{/2,df} * (s /n)
= 2.492 * (17.7 / 25)
Margin of error = E = 8.822
The 98% confidence interval estimate of the population mean is,
- E < < + E
70.2 - 8.822 < < 70.2 + 8.822
61.378 < < 79.022
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