A genetic experiment involving peas yielded one sample of offspring consisting of

429

green peas and

147

yellow peas. Use a

0.01

significance level to test the claim that under the same circumstances,

25%

of offspring peas will be yellow. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.

Question content area bottom

Part 1

What are the null and alternative hypotheses?

A.Upper H 0 : p not equals 0.25 Upper H 1 : p equals 0.25

H0:p0.25

H1:p=0.25

B.Upper H 0 : p not equals 0.25 Upper H 1 : p greater than 0.25

H0:p0.25

H1:p>0.25

C.Upper H 0 : p equals 0.25 Upper H 1 : p greater than 0.25

H0:p=0.25

H1:p>0.25

D.Upper H 0 : p equals 0.25 Upper H 1 : p less than 0.25

H0:p=0.25

H1:p<0.25

E.Upper H 0 : p equals 0.25 Upper H 1 : p not equals 0.25

H0:p=0.25

H1:p0.25

F.Upper H 0 : p not equals 0.25 Upper H 1 : p less than 0.25

H0:p0.25

H1:p<0.25

Part 2

What is the test statistic?

z=enter your response here

(Round to two decimal places as needed.)

Part 3

What is the P-value?

P-value=enter your response here

(Round to four decimal places as needed.)

Part 4

What is the conclusion about the null hypothesis?

A.

Reject

the null hypothesis because the P-value is

lessthanorequalto

the significance level,

.

B.

Failtoreject

the null hypothesis because the P-value is

greaterthan

the significance level,

.

C.

Reject

the null hypothesis because the P-value is

greaterthan

the significance level,

.

D.

Failtoreject

the null hypothesis because the P-value is

lessthanorequalto

the significance level,

.

Part 5

What is the final conclusion?

A.

There

is

sufficient evidence to warrant rejection of the claim that

25%

of offspring peas will be yellow.

B.

There

isnot

sufficient evidence to warrant rejection of the claim that

25%

of offspring peas will be yellow.

C.

There

isnot

sufficient evidence to support the claim that less than

25%

of offspring peas will be yellow.

D.

There

is

sufficient evidence to support the claim that less than

25%

of offspring peas will be yellow.