Please answer all parts of the following question:

DaBahy and Lil Baby are having a heated discussion about which One is the bigger Baby on the music scene (from their names, one would assume that it is clearly DaBaby. But, anyway ...). Five pe0ple on the street are each asked to rate both DaBaby and Lil Baby's music on a scale of 0 to 100. Assume that the responses can be any real number and that the ratings data is normally distributed. The table below contains the responses. _| DaBaby Rating Lil Baby Rating 96 34 Person 1 Person 2 74 43 Person 3 53 33 Person 4 72 31 Person 5 99 45 (a) Suppose DaBaby wants to prove that he is rated strictly higher than Lil Baby by the overall populatiOn. Formulate and test an appropriate null and alternative hypothesis to support his claim. What does the data indicate about the claim? (Hint: If you understand the meaning of the t-statistic, you don't really need a ttable or Excel to make an inference.) (l3) Construct a two-sided 99% condence interval on the difference (among the Whole population) of DaBaby and Li] Baby's average ratings. (c) If we were not able to ask the same people to rate the two rappers, explain how we would have to alter the condence interval in part (b). Further, explain if you would expect the condence interval to be bigger1 smaller, or the same for this kind of analysis