A group of professors at a large university investigated first-year college students' knowledge of astronomy. One concept of interest was the Big Bang theory of the creation of the universe. In a sample of

112

freshman students,

28

believed that the Big Bang theory accurately described the creation of planetary systems. Based on this information, is it correct at the

=0.05

level of significance to state that more than

20%

of all freshman college students believe the Big Bang theory describes the creation of planetary systems?

Question content area bottom

Part 1

Determine the null and alternative hypotheses.

H0:

(1)

(2)

enter your response here

Ha:

(3)

(4)

enter your response here

(Type integers or decimals. Do not round.)

Part 2

Determine the test statistic.

The test statistic is

enter your response here.

(Round to two decimal places as needed.)

Part 3

Determine the p-value.

The p-value is

enter your response here.

(Round to three decimal places as needed.)

Part 4

Determine the proper conclusion.

(5)

H0.

There is

(6)

evidence at the

=0.05

level of significance to indicate the true percentage of freshman college students that believe the Big Bang theory describes the creation of planetary systems

(7)

enter your response here%.

(Type an integer or a decimal. Do not round.)

(1)

p

(2)

<

=

>

(3)

p

(4)

>

=

<

(5)

Do not reject

Reject

(6)

sufficient

insufficient

(7)

differs from

is greater than

does not differ from

is less than