6. This problem set is due on April 4. Suppose that, using a sample consisting of the last 50 years of data ( so, u =50), the average high temperature in the Twin Cities on April 4 is 51.00 degrees. Suppose that the sample standard deviation ( from that 50 years of data) is equal to 7.75 degrees. a.) Using the sample above, find a 95 % condence interval for the true (i.e., population) average high temperature on April 4. (5) Su ose that someone claims that the true ( i.e., population) average high on April 4 is 49.25 degrees. b.) Can you say \" I'm 95 % certain that you're wrong\"? Explain. (3) c.) Can you say \"I'm 71 % certain that you're wrong\"? Explain (calculate a new condence interval to support your answer; note that question # 4 is relevant). (3) Now, suppose that a sample consisting of the last 100 years is used instead. ' The sample statistics, however, stay the same: Sample Mean = 51.00 degrees Sample Standard Deviation = 7.75 degrees Again consider the individual who claims that the true ( i.e., population) average high on April 4 is 49.25 degrees. ' d.) With the new ( larger) data set, can you say \" I'm 95% certain that you're wrong\"? Explain ( calculate a new condence interval, to support your answer). (3) 6.) Explain why your answers to b.) and d.) are different, even though the sample statistics of the data sets are the same. (2)