Question

A machine fills cereal boxes. Each box is to contain 525 grams. The machine is considered to be working properly if in a production run the machine fill value is 525 grams. To check it the machine is working properly each day, a sample of the boxes (size n=12 boxes) of that day's production is selected. The way the machine works is that it is very unlikely to under fill by much, so the main concern is that the machine fill level does not increase. A little extra of the product in each box adds up to a big loss for the company. A sample of one production run gave the following data:

520, 525, 523, 524, 525, 524, 528, 523, 522, 524, 525, 530

Using the above data calculate the p-value for the null hypothesis that the median fill is still at 525g versus the alternative that it has increased. Give your answer to 3 decimal places.

Answer 1

Here the hpothais to be tented is Null wypothanis, H.: Median -525 Alternaive hpothais, HA: Median 7 525 bservahon ValuL (Xi) Xí-525 sign(X-525 -ve 5 20 5 25 523 524 5 25 5 24 5 28 523 5 22 3 A- -ve 2. -ve 525 12 530 +ve number o minun sign Y equivalantly , wkamexen + ob served trachion o minun signs is signi ficantly lem than , is Small oY 2. Thun,the eompute is len than ' e uổi,U reject Ho and con 1o-r = 10.9804.

As the p-value is very high; we fail to reject the null huhypothes and conclude that the median fill is still at 525g.