Question

A certain chemical compound (measured in milligrams) is important in a drug used to promote sleeping. However, too little and the drug won’t be effective and even a slight overdose could have nasty side effects. The ideal amount in each pill is 53 mg. The FDA randomly selects 125 pills that are on the market and finds that the sample mean is 54mg with a standard deviation of 3 mg. Determine if the pills on the marketplace are safe and effective using a 1% significance level.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 53
Alternative Hypothesis, Ha: μ ≠ 53

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (54 - 53)/(3/sqrt(125))
t = 3.727

P-value Approach
P-value = 0.0003

As P-value < 0.01, reject the null hypothesis.

there is sufficient evidence to conclude that the pills on the marketplace are not safe and effective