Need help with part (d) of homework problem #6! THERE IS A TYPO in part (d), it should be H0: mu = 0 versus H1: mu = 1 !! KEEP IN MIND PLEASE!

Please answer thoroughly and show work! Thank you!

6. We are given 5 observations, namely {51.20, 42.88, 35.15, 41.04, 13.68}, for the surface temperatures (in degrees Centigrade) on an asteroid. Assume that these are independent observations from a N (mail) distribution With given variance 02 = 49. Suppose further that we have a prior distribution on ,u that is Normal With mean 0 and variance 36. (d) If only 2 values of u namely 0 and 1 are possible and have prior probabilities 2/3 and 1/3 respectively, test H0 : ,u = 0 versus H1 : ,u = 2. (10+5+10+5=30)