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. =
~ ![t_n_-_1](https://tex.z-dn.net/?f=t_n_-_1)
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> =
~
![t_4_9](https://tex.z-dn.net/?f=t_4_9)
= 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.