Question

Q 5       AMERICAN COMPUTER MACHINES, A LARGE COMPUTER FIRM, HAS BRANCH OFFICES IN SEVERAL MAJOR CITIES OF THE WORLD. FROM PAST EXPERIENCE, ACM KNOWS THAT ITS EMPLOYEES RELOCATE ON THE AVERAGE ONCE EVERY TEN YEARS. DUE TO RECENT POPULATION TRENDS, THE COMPANY WANTS TO DETERMINE IF THE AVERAGE RELOCATION TIME HAS CHANGED ( THAT IS, IS THE AVERAGE RELOCATION TIME DIFFERENT FROM FROM TEN YEARS?) TO DETERMINE IF A CHANGE HAS OCCURRED A RANDOM SAMPLE OF TWENTY FIVE EMPLOYEES WERE INTERVIEWED AND IT WAS FOUND THAT THEIR MEAN RELOCATION TIME WAS 9.5 YEARS WITH S = 4.5 YEARS. DOES THIS SAMPLE RESULT INDICATE A CHANGE HAS OCCURRED IN THE MEAN RELOCATION TIME. ALPHA = 0.05                              
                                      
                                      
                                      
                                      
                                      
                                      
                                      
                                      
                                      
       DETERMINE THE NULL AND ALTERNATIVE HYPOTHESES                              
       DETERMINE THE DECISION RULE, WHAT ARE THE BOUNDARY LINES?                              

Answer 1

Here claim is that mean has changed

So hypothesis is vs

Let us assume that distribution is normal

But as n<30 so we will use t statistics

The t-critical values for a two-tailed test, for a significance level of α=0.05 are

tc​=−2.064 and tc​=2.064

Graphically

As test statistics do not fall in the rejection region we fail to reject the null hypothesis

Hence we do not have sufficient evidence to support the claim that mean is different from 10