Question

1. An agronomist randomly sampled 18 certified organic apples and 42 “regular” (not certified organic) apples. (Multiple varieties were selected.) The organic apples had a mean weight of 3.4 ounces with a standard deviation of 0.4 ounces. The agronomist also confirmed that the weights of the organic apples were roughly normally distributed. The regular apples had a mean weight of 3.9 ounces with a standard deviation of 0.3 ounces. The agronomist will be testing the hypothesis that the mean weight of an organic apple is less than the mean weight of a “regular” apple.

1. Conduct an appropriate hypothesis test of the claim. [Be sure to state the hypotheses, find the test statistic, find the p-value or critical value (either is OK), and draw the appropriate conclusion about the claim.]
2. Why didn’t the agronomist bother to check that the weights of regular apples were roughly normal?
3. If the weights of the organic apples had turned out to be clearly bimodal with a couple of extreme outliers, which test should we have used instead?

Answer 1

Let denote the mean weight of the organic and regular apples respectively.

There is sufficient evidence to support the claim that the mean weight of an organic apple is less than the mean weight of a “regular” apple.

ii) Since sample size for regular apples is large enough (>30), the sampling distribution of sample mean will follow normal distribution using Central limit theorem.