When watching games of men's basketball,have noticed that the players are often tall. I aminterested to find out whether or not men whoplay basketball really are taller than mengeneral. I know that the heights, in metres, of mengeneral have the distribution N(1.73, 0.08). I make the assumption that the heights, X metres.of male basketball players are also normallydistributed, with the same variance as the heightsof men in general, but possibly with a largermeana (a) Write down the null and alternativehypotheses under test. I propose to base my test on the heights of eightmale basketball players who recently appearedfor our local team, and I shall use a 5% level ofsignificance. (b) Write down the distribution of the samplemean, X, for samples of size 8 drawn fromthe distribution of X assuming that the nullhypothesis is true. (c) Determine the critical region for my test,illustrating your answer with a sketch.(d) Carry out the test, given that the mean height of the eight players is 1.765 m. Youshould present your conclusions carefully,stating any additional assumption you needa to make.In fact, the distribution of X is N(1.80, 0.062). (e) Find the probability that a test based on arandom sample of size 8 and using the critical region in part (c) will lead to theconclusion that male basketball players arenot taller than men in general.(MEI)​