Answer Happy

PLEASE ANSWER PART (a) AND (b)
( Prestion 3 - Compulsory 34 marks] random sample of independent random variables (X ..... X.) such that a (/ Consider NiN(4,0%) Vi= 1,...,n. (ii) an (i) Derive an expression for the expectation of the sum S = 1_, X expression for the variance of this same sum S (5) State what distribution (including its parameters) the associated sample mean 151 has. You are not required to prove the result. b) In the context of a study on vehicle exhaust noise levels, the noise levels in decibels) of & random sample of 40 cars were recorded at a specialized automobile test centre. The mean level was 85 decibels with an associated standard deviation of 4 decibels. (i) Calculate a 95% confidence interval for the mean noise level. [6] (ii) Interpret the confidence interval found in (b)(i). 14 (ii) The manager of the test centre explained that the same study carried out the previous year had revealed a mean noise level of 89 decibels. Based on the confidence interval obtained in (b)(i), would the manager have been correct in suspecting the same noise (5) level from the results of the new study? [5] (iv) Suppose one wanted to estimate the mean noise level to within 2 decibels with 9596 confidence. How many cars would one need to include in the study?