7.2(10d)

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

40

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

37.7

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

6.7

milligrams. At

=0.03,

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

Question content area bottom

Part 1

(a) Identify

H0

and

Ha.

Choose the correct answer below.

A.

H0:

40

Ha:

>40

B.

H0:

37.7

Ha:

>37.7

C.

H0:

=40

Ha:

40

Your answer is correct.

D.

H0:

=37.7

Ha:

37.7

E.

H0:

37.7

Ha:

=37.7

F.

H0:

40

Ha:

=40

Part 2

(b) Find the critical value(s). Select the correct choice below and fill in the answer box within your choice.

(Round to two decimal places as needed.)

A.

The critical values are

2.172.17.

Your answer is not correct.

B.

The critical value is

enter your response here.

Part 3

Identify the rejection region(s). Choose the correct answer below.

A.

-404z

RejectH0.

RejectH0.

FailtorejectH0.

A normal curve is over a horizontal axis labeled z from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segments extend to the left of and to the right 0 from the horizontal axis to the curve. The area under the curve the left of the left line segment and to the right of the right lines segment is shaded and labeled Reject H@Sub{0}. The area between the vertical line segments is labeled Fail to reject H@Sub{0}.

Your answer is correct.

B.

-404z

RejectH0.

FailtorejectH0.

A normal curve is over a horizontal axis labeled z from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segment extends to the left of 0 from the horizontal axis to the curve. The area under the curve to the left of the line segment is shaded and labeled Reject H@Sub{0}. The area under the curve to the right of the line segment is labeled Fail to reject H@Sub{0}.

C.

-404z

RejectH0.

FailtorejectH0.

A normal curve is over a horizontal axis labeled z from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segment extends to the right of 0 from the horizontal axis to the curve. The area under the curve to the right of the line segment is shaded and labeled Reject H@Sub{0}. The area under the curve to the left of the line segment is labeled Fail to reject H@Sub{0}.

Part 4

(c) Find the standardized test statistic.

z=enter your response here

(Round to two decimal places as needed.)