If the built-up beam is subjected to an internal moment of M = 75 kN m, determine the

4.3.2 WILCOXON SIGNED-RANK TEST 1) Used for the differences between two samples. In this case we take the differences (D’s) and test the null hypothesis a. H :0Distribution of D’s is symmetric about the nullval∆e against the alternatives of D ▯ values tending to be smaller than▯ or D values tending to be larger th∆n▯ b. Rank the absolute values of the differences c. Calculate the test statistis+, by adding all off differences 2) Note: 3) The test statistic, denoted by W: 4) The null is rejected if 4.3.3 LEVENES TEST FOR VARIANCES 1) Used for comparing more than 2 population variations a. Deals with variances b. The null is that all of these particular variancesare equal c. The alternative is that they are not 2) Levenes test is used because it is the least restrictive, in that, there are no assumptions regarding sample size or distribution. a. Only requirement is that the populations are independent 3) We will use software to calculate because calculation is tedious a. Where N is grand total of observations b. The null is rejected if the p-value is less than alpha 4.4 CONTINGENCY TABLES TEST FOR INDEPENDENCE 1) They are cross-tabulations of frequency counts a. i.e. 2) Notation for contingency tables: th th a. ▯ =▯▯he number in the i row and j column