Handbook of Civil Engineering Calculations

9.98 ENGINEERING ECONOMICS
that under the present method. Thus, the hypotheses are H 0: 3.50 h and 0.64 h;
H 1: < 3.50 h.
2. Compute the properties of the sampling distribution
of the mean as based on the null hypothesis
Apply Eqs. 14 and 15a, giving X – 3.50 h and X – 0.64/40 0.101 h.
3. Compute the critical value of X –
By the central-limit theorem given in the preceding calculation procedure, the sampling
distribution of the sample mean X – may be considered normal, and the sampling distribution
diagram is shown in Fig. 24a. Management has imposed a requirement of 95 percent
probability. Therefore, the null hypothesis is disproved and the alternative hypothesis
validated if the true sample mean has a value less than that corresponding to 95 percent of
all possible samples. In Fig. 24a, locate B such that the area to the right of B 0.95; then
area from A to B 0.95 0.50 0.45. The null hypothesis is to be accepted or rejected
FIGURE 24. Sampling distribution of mean production time corresponding to
three distinct values of the population mean.