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A company uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressings is working properly when 9 ounces are dispensed. The standard deviation of the process is 0.25 ounce. A sample of 60 bottles is selected periodically, and the filling line is stopped if there is evidence that the average amount dispensed is different from 9 ounces. State the null and alternative hypotheses. Is there evidence that the population average amount is different from 9 ounces? Use a 0.01 level of significance. Suppose that the average amount dispensed in a particular sample of 60 bottles is 8.783 ounces. 

          A company uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressings is working properly when 9 ounces are dispensed. The standard deviation of the process is 0.25 ounce. A sample of 60 bottles is selected periodically, and the filling line is stopped if there is evidence that the average amount dispensed is different from 9 ounces. State the null and alternative hypotheses. Is there evidence that the population average amount is different from 9 ounces? Use a 0.01 level of significance.
Suppose that the average amount dispensed in a particular sample of 60 bottles is 8.783 ounces.
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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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A company uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressings is working properly when 9 ounces are dispensed. The standard deviation of the process is 0.25 ounce. A sample of 60 bottles is selected periodically, and the filling line is stopped if there is evidence that the average amount dispensed is different from 9 ounces. State the null and alternative hypotheses. Is there evidence that the population average amount is different from 9 ounces? Use a 0.01 level of significance. Suppose that the average amount dispensed in a particular sample of 60 bottles is 8.783 ounces.
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Transcript

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00:01 So for this problem, since we are testing to see if the mean value is different from nine ounces, we'd have that our null hypothesis is that the mean value is equal to nine ounces, and our alternate hypothesis is that the mean value simply does not equal nine ounces.
00:19 So this is going to be a two -tailed test, and we're told that we have alpha equals 0 .01 as our level of significance.
00:28 So i'll start off by finding our rejection region.
00:33 The rejection region is going to be all z scores, or actually i'll put it this way, r is going to be the set of z scores, such that the magnitude of the z score is greater than z for a proportion of 1 minus alpha over 2 in the tail.
00:53 So that would be 0 .99, or 0 .005 in the tail.
01:00 So if we want a...
01:02 So i'm just going to use my software here for finding that z value.
01:06 So i'd put in normal distribution.
01:09 0 .005.
01:10 I'll get a negative value, but we really just care about what the proportion in the tail is...
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