A coffee shop claims that its fresh-brewed drinks have a mean caffeine content of 80 milligrams per five ounces. You work for a city health agency and are asked to test this claim. You find that a random sample of 42 five-ounce servings has a mean caffeine content of 83 milligrams and a standard deviation of 7.5 milligrams. At= 0.05, do the evidence suggest that the mean caffeine content is in factdifferentthan 80 milligrams per five ounces?

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.