Question

Means and Slopes-The process of producing cardiac medicine yields capsules with varying amounts of the active ingredient. It is claimed that the average amount of active ingredient per tablet is at least 50 milligrams. The Drug Enforcement Administration tests a random sample of 100 tablets. The mean content of the active ingredient for this sample is 30.5 milligrams and the standard deviation is 7 milligrams. What is the approximate p-value for the appropriate test?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 50
Alternative Hypothesis, Ha: μ < 50

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (30.5 - 50)/(7/sqrt(100))
t = -27.857

P-value Approach
P-value = 0