Question

11-E2. I have one year of weekly data on the number of defective components per thousand supplied to a customer. The mean is 7.7, the standard deviation is 4.6 and the standard error of the mean is 0.638. The benchmark defective rate is 8.5.

1. Explain, in words that would be understood by a non-expert, what the 4.6 and 0.638 figures tell us.
2. What assumptions underlie the interpretation of the figures in part (a)?
3. Is the customer receiving better than the benchmark? Since 7.7 is less than 8.5, is this a question even worth asking?
4. Suppose that the 8.5 figure comes from last year's database across 28 customers, and includes 28x52=1456 recorded defective counts per 1000, the average of which was 8.5 and the standard deviation of which was 5.1. Is the customer receiving better quality than last year?

Answer 1

a) Standard deviation (sd) denotes the spread from the mean. Hence, 4.6 represents how much the number of defective components per thousand are spread about mean 7.7.

Standard error of mean represents the sd of estimator of mean. Hence, the population mean is 7.7 with a spread of 0.638 that this is the true mean. In this case, the deviation is due to the estimation of the mean and not the the process itself.

b) Assumption: Process follows Normal distribution.

c) Yes, the customer is receiving better than the benchmark.

Yes, the question is worth asking, because, the mean is 7.7 does not necessarily imply that everyone will receive satisfactory products. We can calculate the probability that a customer receives better than benchmark quality.

d) Using the test of difference of mean with given sd, we can see that customers are receiving better quality than the last year.