Question

A company that makes cola drinks states that the mean caffeine content per​ 12-ounce bottle of cola is

5555

milligrams. You want to test this claim. During your​ tests, you find that a random sample of thirty​ 12-ounce bottles of cola has a mean caffeine content of

52.952.9

milligrams. Assume the population is normally distributed and the population standard deviation is

7.87.8

milligrams. At

alphaαequals=0.050.05​,

can you reject the​ company's claim? Complete parts​ (a) through​ (e).

​(a) Identify

Upper H 0H0

and

Upper H Subscript aHa.

Choose the correct answer below.

A.

Upper H 0H0​:

muμless than or equals≤5555

Upper H Subscript aHa​:

muμgreater than>5555

B.

Upper H 0H0​:

muμnot equals≠5555

Upper H Subscript aHa​:

muμequals=5555

C.

Upper H 0H0​:

muμnot equals≠52.952.9

Upper H Subscript aHa​:

muμequals=52.952.9

D.

Upper H 0H0​:

muμequals=5555

Upper H Subscript aHa​:

muμnot equals≠5555

E.

Upper H 0H0​:

muμequals=52.952.9

Upper H Subscript aHa​:

muμnot equals≠52.952.9

F.

Upper H 0H0​:

muμless than or equals≤52.952.9

Upper H Subscript aHa​:

muμgreater than>52.9

Answer 1

(a)

Since we don't have any clue whether we are testing for more cola or less cola than the specified, we will go with a two-tailed test i.e. Option-D

H₀: μ = 55
H_A: μ ≠ 55