In a recentyear, a poll asked 2360

2360 random adult citizens of a large country how they rated economic conditions. In thepoll, 28

28% rated the economy asExcellent/Good. A recent media outlet claimed that the percentage of citizens who felt the economy was inExcellent/Good shape was 25

25%. Does the poll support thisclaim?

a)

Test the appropriate hypothesis. Find a 99

99% confidence interval for the proportion of adults who rated the economy asExcellent/Good. Check conditions.

b)

Does your confidence interval provide evidence to support theclaim?

c)

What is the significance level of the test inb? Explain.

a) Let p be the proportion of adult citizens who felt the economy was inExcellent/Good shape. What are the null and alternative hypotheses for thetest?

A.

H0: pequals

=0.28

0.28 vs. HA: pless than

<0.28

0.28

B.

H0: pequals

=0.25

0.25 vs. HA: pnot equals

0.25

0.25

C.

H0: pequals

=0.28

0.28 vs. HA: pnot equals

0.28

0.28

D.

H0: pequals

=0.25

0.25 vs. HA: pgreater than

>0.25

0.25

Check the conditions. Which of the following conditions aresatisfied? Select all that apply.

A.

Less than10% of the population was sampled.

B.

The data are independent.

C.

There are more than 10"successes" and 10"failures."

D.

The sample is random.

Find a 99

99% confidence interval for the proportion of adults who rated the economy asExcellent/Good. Select the correct choice below and fill in any answer boxes within your choice.

A.

left parenthesis nothing comma nothing right parenthesis

,

(Round to three decimal places asneeded.)

B.

The conditions of a confidence interval are not satisfied.

b) Does your confidence interval provide evidence to support theclaim?

A.

Yes

Yes. Since pequals

=0.25

0.25 is

is within theinterval, there is evidence to support

tosupport the

the claim

claim.

B.

Yes

Yes. Since pequals

=0.25

0.25 is not

isnot within theinterval, there is evidence to support

tosupport the

the claim

claim.

C.

No

No. Since pequals

=0.25

0.25 is

is within theinterval, there is evidence that the proportion is

thattheproportionis not

not p equals 0.25

p=0.25.

D.

No

No. Since pequals

=0.25

0.25 is not

isnot within theinterval, there is evidence that the proportion is

thattheproportionis not

not p equals 0.25

p=0.25.

E.

The confidence interval cannot be found because not all of the conditions are satisfied.

c) The significance level is alpha

equals

=

34

34, because the test is a two

two

one

-sided test and is based on a 99

99% confidence interval.