Hi, The solution gives an explanation stating that the null hypo. is true as the interval given contains zero. But the given interval is a two sided symmetric interval whereas the question was to test the hypo. against improvement(i.e one sided test)... So do we have to calculate the one sided interval or just continue as given in the solution ?(although both give the same conclusion)
We don't have to test anything here, just infer from the given data. The value of regression parameter for new tuition method (b3) is negative (-0.05). So by first looks, it does seem to have reduced the hazard rate of children giving up on their music classes. But when we look at it's C.I. which is [-0.15,0.05], it seems to have 0 in it (which will result in unchanged hazard) and positive values as well (which will increase the hazard rather than decreasing it). So, at 5% level of significance we cannot conclude that the "New tuition method" has decreased the hazard rate of exits.. Now suppose, if this was a 90% symmetric C.I. then surely it would've have been smaller than the 95% one. Say if it was [-0.09,-0.01]. Now this C.I. doesn't contains 0. So we would've written that "At 10% level of significance, it's reasonable to conclude that the 'new tuition method' seems to have increased the persistency rates or decreased the hazard rate of exits" Hope this helps..
