The Berg Balance Scale (BBS), named after its developer Katherine Berg, is a popular clinical test of a person's static and dynamic balance abilities. It is scored on a scale of O to 56; the higher the value, the better the score. The cut-off score is 45, which means that a score less than 45 indicates a greater risk of falling. The file BBS Older contains data for 20 older patients at a hospital: 43 40 32 38 32 34 46 33 39 34 48 42 49 40 40 35 40 40 39 a. At the 0.05 level of significance, is the re evidence that the pop- ulation mean BBS value is less than 40? b. What assumption about the population distribution is needed in order to conduct the t test in (a)? c. Construct a boxplot or a normal probability plot to evaluate the assumption made in (b). d. Do you think that the assumption needed in order to conduct the t test in (a) is valid? Explain.