Question

A genetic experiment involving peas yielded one sample of offspring consisting of 411 green peas and 140 yellow peas. Use a 0.01 significance level to test the claim that under the same​ circumstances, 27​% 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.

What are the null and alternative​ hypotheses?

A.

Upper H 0 : p not equals 0.27

Upper H 1 : p equals 0.27

B.

Upper H 0 : p not equals 0.27

Upper H 1 : p greater than 0.27

C.

Upper H 0 : p not equals 0.27

Upper H 1 : p less than 0.27

D.

Upper H 0 : p equals 0.27

Upper H 1 : p less than 0.27

E.

Upper H 0 : p equals 0.27

Upper H 1 : p not equals 0.27

F.

Upper H 0 : p equals 0.27

Upper H 1 : p greater than 0.27

What is the test​ statistic?

zequals

nothing

​(Round to two decimal places as​ needed.)

What is the​ P-value?

​P-value=_____

​(Round to four decimal places as​ needed.)

What is the conclusion about the null​ hypothesis?

A.

Reject the null hypothesis because the​ P-value is less than or equal tothe significance​ level, alpha.

B.Fail to reject the null hypothesis because the​ P-value is less than or equal to the significance​ level, alpha.

C.Reject the null hypothesis because the​ P-value is greater thanthe significance​ level, alpha.

D.Fail to reject the null hypothesis because the​ P-value is greater than the significance​ level, alpha.

What is the final​ conclusion?

A.There is sufficient evidence to support the claim that less than 27% of offspring peas will be yellow.

B.There is sufficient evidence to warrant rejection of the claim that 27% of offspring peas will be yellow.

C.There is not sufficient evidence to support the claim that less than 27​% of offspring peas will be yellow.

D.There is not sufficient evidence to warrant rejection of the claim that 27% of offspring peas will be yellow.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.27

H_a : p 0.27

= x / n = 140 / 411 = 0.3406

P₀ = 0.27

1 - P₀ = 0.73

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.3406 - 0.27 / [(0.27 * 0.73) / 411]

= 3.225

= 3.23

P(z > 3.225) = 1 - P(z < 3.225) = 0.0006

P-value = 2 * 0.0006 = 0.0012

= 0.01

P-value <

Reject the null hypothesis because the​ P-value is less than or equal tothe significance​ level, alpha.

B.There is sufficient evidence to warrant rejection of the claim that 27% of offspring peas will be yellow.