A weight loss program claims that program participants have a mean weight loss of at least 12 pounds after 1 month. You work for a medical association and are asked to test this claim. A random sample of 30 program participants and their weight losses (in pounds) after 1 month is listed in the table below. Assume the population standard deviation is 3. At alphaequals0.03, do you have enough evidence to reject the program's claim? Complete parts (a) through (e). 5.4 5.9 6.5 6.6 7.3 7.5 7.8 8.3 8.3 8.5 8.6 9 9.2 9.4 9.6 9.9 10.3 10.5 10.6 10.6 10.7 11.2 11.4 11.8 11.8 12.1 12.7 12.7 13.9 15.9 (a) Identify

Upper H 0H0

and

Upper H Subscript aHa.

Choose the correct answer below.

A.

Upper H 0H0:

munot equals1212

Upper H Subscript aHa:

muequals=1212

B.

Upper H 0H0:

muless than or equals1212

Upper H Subscript aHa:

mugreater than>1212

C.

Upper H 0H0:

mugreater than>1212

Upper H Subscript aHa:

muless than or equals1212

D.

Upper H 0H0:

mugreater than or equals1212

Upper H Subscript aHa:

muless than<1212

E.

Upper H 0H0:

muequals=1212

Upper H Subscript aHa:

munot equals1212

F.

Upper H 0H0:

muless than<1212

Upper H Subscript aHa:

mugreater than or equals1212

(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

plus or minusenter your response here.

B.

The critical value is

negative 2.172.17.

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

A.

-404z

Reject Upper H 0 .RejectH0.

Fail to reject Upper H 0 .FailtorejectH0.

Reject Upper H 0 .RejectH0.

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}.

B.

-404z

Reject Upper H 0 .RejectH0.

Fail to reject Upper H 0 .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

Reject Upper H 0 .RejectH0.

Fail to reject Upper H 0 .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}.

(c) Find the standardized test statistic.

zequals=negative 3.123.12

(Round to two decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis.

A.

Since z

isis

in the rejection region,

fail to rejectfailtoreject

the null hypothesis.

B.

Since z

isis

in the rejection region,

rejectreject

the null hypothesis.

C.

Since z

is notisnot

in the rejection region,

rejectreject

the null hypothesis.

D.

Since z

is notisnot

in the rejection region,

fail to rejectfailtoreject

the null hypothesis.

(e) Interpret the decision in the context of the original claim.

At the

33%

significance level, there

is not

enough evidence to

reject

the program's claim that program participants have a mean weight loss

greater than or equal to

1212

pounds after 1 month.