In order to study the amounts owed to the city, a city clerk takes a random sample of 16 files from a cabinet containing a large number of delinquent accounts and finds the average amount owed to the city to be $259 with asamplestandard deviation of $36. It has been claimed that the true mean amount owed on accounts of this type isgreater than$250. If it is appropriate to assume that the amount owed is a normally distributed random variable, test the claim atmu= 0.01.

Your answer must include:i)null and alternative hypotheses;ii)statement of assumptions;iii)calculation of the test statistic;iv)calculation of theP-value;v)decision in terms of the null hypothesis; andvi)conclusion in the context of the problem.