Question

Suppose a small company that manufactures cereal bars own two scales that weigh their products (say A and B). Quality control manager in this company is concerned that scale A is erroneous. He takes a sample of 20 cereal bars and weigh each of them using both scales A and B. Assume that you were given a spread sheet that include weights of the 20 cereal bars reported by two scales.

Explain how you would approach testing the QC managers’ concern. What type of tests/CI you would construct to help him make a decision? Mention of any assumptions you would check or any graphing techniques you would use to display the data.

Answer 1

First of all we have to assume that the weights are normally distributed.

To verify this assumption we have to draw the normal probability plot in which frequency is plotted against normal quantiles. If this shows the linear pattern in the points then we can say that the data follows the normal distribution. If it is normal distribution then go forward.

Here the manufacturer wants to know if the weights on scale A and scale B are equal or not. For this consider the null hypothesis that

Where is the population mean of weights on scale A.    is the population mean of weights on scale B.

Then use t test for independent samples where sample size is 20 and population standard deviation is unknown. Also we can use confidence interval for population mean using pivotal quantity same as the test statistic of t test for independent samples. If the confidence interval contains the value zero ( because null hypothesis is difference between population means of weights is zero) then manufacturer would conclude that scale is not erroneous.