Question

A box of cereal is listed as containing 10 ounces of oat-nut clusters. A consumer-rights groups found that a random sample of 76 boxes had an average weight of Y¯ = 9.876 ounces with a sample standard deviation of S = 0.483. Is there evidence at the α = 0.01 level that the boxes are being systematically under-filled? Use p-value to draw the conclusion.

Answer 1

Sample size = n = 76

Sample mean = = 9.876

Standard deviation = s = 0.483

Claim: The boxes are being systematically under filled.

The null and alternative hypothesis is

Level of significance = 0.01

Here population standard deviation is unknown so we have to use t-test statistic.
Test statistic is

Degrees of freedom = n - 1 = 76 - 1 = 75

P-value = P(T < - 2.24) = 0.0141

P-value > 0.01 we fail to reject null hypothesis.

Conclusion:

A box of cereal is listed as containing 10 ounces of oat-nut clusters.