Question

A baby food company claims that on the average the product contains 6.0 grams of protein per bottle. A random sample of 13 bottles of the product was taken and the protein measurements are as follows.

5.1 4.9 6.0 6.4 5.7 4.8 6.2 6.0 5.9 5.6 5.5 5.8 5.3

1. Find the sample mean x¯ and the sample standard deviation s.
2. Assume that the protein content per bottle obeys an N (µ, σ²) distribution with σ unknown. Give the study’s objective in terms of H₀ and H_A and then perform a test at the α = 0.05 level.
3. In the foregoing analysis (you just performed) you might reject H₀ even when the mean protein content is exactly 6.0 gram per bottle as claimed. What is the name for this kind of mistake? What measure can be taken to control the probability of this kind of mistake?

Answer 1