it has been claimed that 60% of All solar heat installations Test 1 AET 395- Fal
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it has been claimed that 60% of All solar heat installations Test 1 AET 395- Fall 2017 Print Name: - Sign 15. Test the hypothesis that the average content of containers of a lu bricant is 1o liters if the contents of a containers are 1 0.2, 9. 7, 1 0.1 , 9.8, 9.9, 10.4, 10.3, and 9.8 liters. 10·1, 1 03, data X = 1 0.06; and the standard deviation-S-0 2459. Use a 0.01 leve that the distribution of contents is normal. l of significance and assume 1 pts) -(1 pts) (1 pts) (2 pts) omputation: (3 pts)Explanation / Answer
Our hypothesis is that the content of a container is 10 liters. u = 10.
Our alternative is that the contents of a container is not 10 liters (u does not equal 10).
X = 10.06 ,S = .2459, a = .01 ,n = 10.
Using T test:
T = (X - u)/(S/Sqrt(n)) = (10.06 - 10)/(.2459/3.1623) = .06/.0777 = .7717.
Since our alternative is two-sided we check for values both above and below our hypothesis so we need the probability that |T| >= .7717, and we use the Student t-distribution with 9 degrees of freedom.
p = P(|T| >= .7717) = 2*P(T >= .7717) = somewhere in the range (.4, .6).
So our p-value is in the range (.4, .6).
Results and Conclusions: Our p-value in the range of (.4, .6) is not significant at the .01 level of significance. Based on this information we fail to reject our hypothesis. We conclude that there is not enough evidence to state the average contents of the containers is anything but 10 liters.
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