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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.
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