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Answer:
We conclude that the mean amount packaged is equal to 8.17 ounces.
Step-by-step explanation:
We are given that in a particular sample of 50 packages, the mean amount dispensed is 8.171 ounces, with a sample standard deviation of 0.052 ounces.
Let = <u><em>population mean amount packaged.
</em></u>
So, Null Hypothesis, :
= 8.17 ounces {means that the mean amount packaged is equal to 8.17 ounces}
Alternate Hypothesis, :
8.17 ounces {means that the mean amount packaged is different from 8.17 ounces}
The test statistics that will be used here is <u>One-sample t-test statistics</u> because we don't know about the population standard deviation;
T.S. = ~
where, = sample mean amount dispensed = 8.171 ounces
s = sample standard deviation = 0.052 ounces
n = sample of packages = 50
So, <u><em>the test statistics</em></u> = ~
= 0.1359
The value of t-test statistics is 0.1359.
<u>Also, the P-value of test-statistics is given by;</u>
the meaning of the p-value is that the p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.001 ounces away from8.17 if the null hypothesis is true.
P-value = P( > 0.136) = More than 40% {from the t-table}
Since the P-value of our test statistics is more than the level of significance of 0.01, so <u><em>we have insufficient evidence to reject our null hypothesis</em></u> as it will not fall in the rejection region.
Therefore, we conclude that the mean amount packaged is equal to 8.17 ounces.