An article in the ASCE Journal of Energy Engineering (1999, Vol. 125, pp. 59-75)
ID: 3150168 • Letter: A
Question
An article in the ASCE Journal of Energy Engineering (1999, Vol. 125, pp. 59-75) describes a study of the thermal inertia properties of autoclaved aerated concrete use; as a building material. Five samples of the material were tested in a structure, and the average interior temperatures (degree C) reported were as follows: 23.01, 22.22, 22.04, 22.6. and 22.59. Test the hypothesis H_0: mu = 22.5 versus H_1: mu notequalto 22.5, using a = 0.05. Compute the test statistic, - 0.0237 0.0237 0.01958 -0.01958 What region supports H_0? -2.132Explanation / Answer
Hi! I used these data:
23.01
22.22
22.04
22.62
22.59
If some data are cut from this picture, please resubmit this question together with the data. That way we can continue helping you! Thanks!
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A)
Formulating the null and alternative hypotheses,
Ho: u = 22.5
Ha: u =/ 22.5
As we can see, this is a two tailed test.
Getting the test statistic, as
X = sample mean = 22.496
uo = hypothesized mean = 22.5
n = sample size = 5
s = standard deviation = 0.378325257
Thus, t = (X - uo) * sqrt(n) / s = -0.023641752 [ANSWER, TEST STATISTIC]
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b)
Thus, getting the critical t,
df = n - 1 = 4
tcrit = +/- 2.776445105
Hence, the region is
OPTION C: -2.776 < t < 2.776 [ANSWER]
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c)
Also, the p value is, as this is two tailed,
p = 0.98227075 [ANSWER]
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d)
As P > 0.05, we FAIL TO REJECT THE NULL HYPOTHESIS.
Hence, there is no significant evidence that the mean temperature is not 22.5 degrees Celcius at 0.05 level. [CONCLUSION]
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