I know the answer, but no matter what I do I cannot obtain the same results. This is the problem below:
A machine fills milk bottles, the mean amount of milk in each bottle is supposed to be 32 Oz with a standard deviation of 0.06 Oz. Suppose the mean amount of milk is approximately normally distributed. To check if the machine is operating properly, 36 filled bottles will be chosen at random and the mean amount will be determined.
Find the power if the true mean is 31.97
First, I found the rejection regions: Lower Region: (x-32) / (.06/sqrt(36) < -1.96 --> x < 31.9804
Upper rejection region: (x-32) / (.06/sqrt(36) > 1.96 --> x > 32.0196
So then I did this:
31.9804 - 31.97/.06 = .173
32.0196 - 31.97/.06 = .826
On the Z-table .173 gives me a p-value of .4325 and .826 gives me a p-value of about .79. The sum of these scores should give me the power.
The answer according to the worksheet is that .8508 and I used a calculator and this is true. However, no matter what I am doing I can't get that.
Can someone please tell me what I am doing wrong.
Thank you!
A machine fills milk bottles, the mean amount of milk in each bottle is supposed to be 32 Oz with a standard deviation of 0.06 Oz. Suppose the mean amount of milk is approximately normally distributed. To check if the machine is operating properly, 36 filled bottles will be chosen at random and the mean amount will be determined.
Find the power if the true mean is 31.97
First, I found the rejection regions: Lower Region: (x-32) / (.06/sqrt(36) < -1.96 --> x < 31.9804
Upper rejection region: (x-32) / (.06/sqrt(36) > 1.96 --> x > 32.0196
So then I did this:
31.9804 - 31.97/.06 = .173
32.0196 - 31.97/.06 = .826
On the Z-table .173 gives me a p-value of .4325 and .826 gives me a p-value of about .79. The sum of these scores should give me the power.
The answer according to the worksheet is that .8508 and I used a calculator and this is true. However, no matter what I am doing I can't get that.
Can someone please tell me what I am doing wrong.
Thank you!