The cholesterol level for all adult men living in Penang is known to be normally distributed.Twelve adult men from Penang are randomly chosen and the cholesterol level are recorded as below:

190 175 221195 204 186

212 199 213182 210 180

(a) Calculate the unbiased estimates of population mean and standard deviation of cholesterol level of men in Penang.

(4 marks)

(b) A medical officer claimed that the cholesterol level of men in Penang is different from 185. Test at 5% level of significance whether the claim is true.

(8 marks)