1. Define the following terms in a sentence (or short paragraph) and state a formula if appropriate (this question is worth 5 marks).

i. Type II Error ii. Power of a Test

iii. Goodness of Fit Test iv. P-value

v. Simple Regression Analysis

1. A coin operated coee machine is set to pour 8 oz per cup. A random sample of the weights of a number of cups is as follows: 8.40, 8.25, 8.05, 7.84, 7.36, 8.54, 7.56, 7.56, 8.02, 7.39, 8.34, 8.56.

Test the hypothesis that the machine is delivering at the level set by the manufacturer. Use a 0.01 level of significance (this question is worth 2 marks).

1. Two dierent brands of milk are randomly sampled, and the fat content in each bottle of milk is determined. Twenty-six bottles of Brand A milk yielded an average fat content of X̄1 = 25 grams withs21 = 4, and thirty one bottles of Brand B yielded an average fat content of X̄2 = 25.8 grams withs2= 7 (this question is worth 3 marks).

Test the hypothesis that both brands have identical average fat content at the 5% level of significance.

1. To compare two programs for training industrial workers to perform a skilled job, 20 workers are included in an experiment. Of these, 10 are selected at random and trained by method 1; the remaining 10 are trained by method 2. After completion of training, all the workers are subjected to a time-and-motion test that records the speed of performance of a skilled job. The following time, as measured in minutes, is obtained.

Sample Solution