SOLUTION: The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 54.2 for a sample of size 362

Question 1204414: The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 54.2 for a sample of size 362 and standard deviation 17.4.
Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% 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).
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
sample size is 362.
sample mean is 54.2
sample stansard deviation is 17.4
using the t-score, critical t-score with 361 degrees of freedom (sample size minus 1) is equal to plus or minus 1.9666.
t-score formula is t = (x-m)/s
t is the t-score
x is the critical mean
m is the sample mean
s is the standard error

standard error = standard deviation / sqrt(sample size) = 17.4 / sqrt(362) = .9145.
on the high side, t=(x-m)/s becomes 1.9666 = (x-54.2)/.9145.
solve for x to get x = 1.9666 * .9145 + 54.2 = 55.9985
on the low side, t = (x-m)/s becomes -1.9666 = (x-54.2)/.9245.
solve for x to get x = -1.9666 * .9145 + 54.2 = 52.4015.
round to 1 decimal place to get:
the 95% confidence interval is between 52.4 and 56 points at 95% confidence level.
your tri-linear equality would be 52.4 <= x <= 56.
since the variable is continuous, then some sticklers will say 52.4 < x < 56 bcause the value can never be exactly a specific value.

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