Question

A company manufactures pens which are packaged and sold in boxes of 20 pens each. The company produces black, red and blue colour pens in the ratio 5:3:2. To ensure that the manufacturing process is working correctly, the plant manager decided to sample 10 boxes from the last 300 boxes that were manufactured and to perform quality checks on these 10 boxes.
6.1 Explain to the manager how she can select a stratified random sample of 10 boxes from the 300 boxes. (6)
A production line fills milk carton on average with 1 litre of long-life milk and a
standard deviation of 0.016 litres. The production line manager sampled 50 cartons at
random from the production belt and found that the average volume of milk for those
50 cartons were 1.006 litres.

6.2 State the mean of the sampling distribution of the sample mean. (1)
6.3 Calculate the standard error of the sampling distribution of the sample mean. (2)
6.4 Calculate the corresponding z-score for the sample mean of 1.006 litres. (3)

Answer 1

6.1: She can select by stratified sampling. Since the ratio of black, red and blue pens is 5:3:2, out of 10, 5 black boxes, 3 red boxes and 2 blue boxes need to be selected randomly from the population. This ensures that we are having an unbiased sample with same weights given to colours as their population occurrences!