Handbook of Civil Engineering Calculations

that under the present method. Thus, the hypotheses are // 0 : JJL = 3.50 h and a = 0.64 h;
H 1 IfJL <3.50h.

2. Compute the properties of the sampling distribution
   of the mean as based on the null hypothesis
   Apply Eqs. 14 and 15«, giving JJL^ = 3.50 h and a^ = 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 distribu-
   tion 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 val-
   idated if the true sample mean has a value less than that corresponding to 95 percent of all
   possible samples. In Fig. 24«, 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 accord-
   ing to whether the true value of X lies to the right or left of B, respectively, and the re-

Rejection region Acceptance region

Area=0.05

FIGURE 24. Sampling distribution of mean production time corresponding to

three distinct values of the population mean.