An article in the ASCE Journal of Energy Engineering (1999, Vol. 125, pp. 59–75)

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 used as a
building material. Five samples of the material were tested in
a structure, and the average interior temperatures (°C) reported
were as follows: 23.01, 22.22, 22.04, 22.62, and 22.59.
Test the hypotheses H0: = 22.5 versus H1: 22.5, using
= 0.05.

a) Compute the sample mean and the sample standard deviation

b) Test the hypotheses H0: = 22.5 versus H1: 22.5, using
= 0.05. Use traditional method, that is find the critical region and make a decision based on this. Show all of your work and clearly state your conclusion.

c) Use the P-value method, that is find the P-value and make a decision based on this value. Show all of your work and clearly state your conclusion.

Explanation / Answer

a)

b)

As test statistics t does not lie in the rejection region, failed to reject the null hypothesis

c)

p-value = 0.4911

As p-value is greater than significance level of 0.05, we failed to reject the null hypothesis

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