Hypothesis testing was performed for the four variables which influence s for additional analysis calculations as follows.

The mean of the population for each random variable was tested against the value given in Table 1 in the problem statement. In order to analyze the means, hypothesis testing was used. The procedure followed for each is outlined below:

1. Formulate hypotheses:

H_o: m=m_o

H_A: m<m_o

 

 

2. Select the appropriate model:

Test statistic z:

 



 

3. Select level of significance: 5% level of significance is selected for this test.

 

4. Compute test statistic estimate: The test statistic is computed for all variables and the results are listed below in table 9.

 

5. Define the region of rejection: -z_a = -F ^-1(1-a) = -1.645 The region of rejection consists of all values of Z less than -1.645.
6. Select the appropriate hypothesis.

The probability distributions for the random variables c, M, I, and f_y were analyzed to determine whether the random numbers generated followed the given distributions from Table 1 in the problem statement. The chi-square test was performed on each of the random variables using the procedure described for the chi-square test for the goodness of fit of s. The hypotheses used indicated whether the variable followed a normal or lognormal distribution, depending on the given distribution type. The level of significance was kept at 5% and the degrees of freedom equal to the number of histogram bins in each corresponding histogram less k, where k is the degrees of freedom. The results of the chi-square test for goodness of fit of the random variables are listed in Tables 10-1 through 10-4.

Goodness of fit of c (Table 10-1)

Goodness of fit of M (Table 10-2)

Goodness of fit of I (Table 10-3)

Goodness of fit of fy (Table 10-4)