Question

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

1- 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 α = 0.02, do the evidence suggest that the mean caffeine content is in fact different than 80 milligrams per five ounces?

2- An environmental conservation agency recently claimed that more than 30% of Canadian consumers have stopped buying a certain product because the manufacturing of the product pollutes the environment. You want to test this claim. To do so, you randomly select 980 Canadian consumers and find that 314 have stopped buying this product because of pollution concerns. At α = 0.04, can you support the agency’s claim?

Answer 1

1)

i)

ii)

data should follow normal distribution with in the population

data is independent on each other value.

iii)

iv)

p value = 2*P( t>2.592) = 0.0132 -------------at df = n-1 = 42-1 = 41

v)

vi)

there is enough evidence to conclude that the mean caffeine content is in fact different than 80 milligrams per five ounces.

we are supposed to answer one question only as per guidelines.pleast post remaing questions separately.