Question

A certain cold medication must contain the amount of the active ingredient as 25 mg per dose to be
effective. If the medication contains more than 25 mg per dose, it’s dangerous to health. If it is less than
25 mg per dose, the medication is not effective. A random sample of 75 doses was taken to a lab and
analyzed to determine the actual amounts of the active ingredient in each of these 75 doses. They
found 24.82 mg active ingredients per dose with standard deviation 0.71 mg.

a. Is the 25 mg a parameter or a statistics? Is the 24.82 mg parameter or a statistic?

b. The medication won’t be approved if the mean amount of the active ingredient is not 25mg. State
the null and alternative hypotheses.

c. Use the Minitab output below to test the claims. Use both outputs (T-Test of the Mean, and T
Confidence Intervals) in your decision. Write your conclusions in context.

T-Test of the Mean
Variable N Mean St. Dev T P
INGR 75 24.82 0.71 -2.2 0.031
T Confidence Intervals
Variable N Mean St Dev 95.0 % CI
INGR 75 24.82 0.71 (24.657, 24.983)

d. Is the confidence interval valid if the distribution from which the 55 measurements were taken is not
normally distributed? Explain briefly.

Answer 1

a) Parameters are numbers that summarize data for an entire population. Statistics are numbers that summarize data from a sample.

So, 25 mg a parameter and  24.82 mg is statistic

b)

Null: μ = 25

Alt: μ ≠ 25

c)

p = 0.031 which is less than alpha (0.05)

Null is rejected

THus, mean is not equal to 25 mg

95% CI does not include 0 as (24.657, 24.983)

So, null is rejected

d)

This interval is only exact when the population distribution is normal. For large samples from other population distributions, the interval is approximately correct by the Central Limit Theorem.

Valid as sample size is greater than 30