Cereal boxes ~ A large box of corn flakes claims to contain 510 grams of cereal. Since cereal boxes must contain at least as much product as their packaging claims, the machine that fills the boxes is set to put 517 grams in each box. The machine has a known standard deviation of 4 grams and the distribution of fills is known to be normal. At random intervals throughout the day, workers sample 2 boxes and weigh the cereal in each box. If the average is less than 512 grams, the machine is shut down and adjusted.

1. How often will the workers make a Type I error with this decision rule and the hypotheses: H0:=517 vs. Ha:<517

Probability of a Type I error = ??? ( I did this and I got .02275 and it is wrong!) Need to round to 4 decimal places.

2. Arka and Sikta both work at the plant and are dissatisfied by the Type I error rate in part 1.

Arka argues the decision rule should be changed such that workers will only shut down the factory if the average is less than 510 grams. Sikta believes the plant should keep the same decision rule, but sample 14 boxes for each quality control check, rather than only 2. Which option will result in a smaller Type I error rate? (Based on above I had Arkas option and that was wrong too., so it is NOT A.)

A. Arka's option

B. Sikta's option

C. Both options give the same Type I error rate

3. Using Arka's decision rule, what is the power of the hypothesis test if the machine is actually filling boxes with an average of 510 grams? That is, calculate the chance of observing a sample mean less than 510 if the true mean is 510.

Power = ????? (I did this problem and I get .9962, and it is wrong!) Has to be rounded to 4 decimals.