Question

A genetic experiment involving peas yielded one sample of offspring consisting of 416 green peas and 165 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 less than 0.27

B.

Upper H 0 : p equals 0.27

Upper H 1 : p not equals 0.27

C.

Upper H 0 : p not equals 0.27

Upper H 1 : p greater than 0.27

D.

Upper H 0 : p equals 0.27

Upper H 1 : p less than 0.27

E.

Upper H 0 : p not equals 0.27

Upper H 1 : p equals 0.27

F.

Upper H 0 : p equals 0.27

Upper H 1 : p greater than 0.27

What is the test​ statistic? ​(Round to two decimal places as​ needed.)

What is the​ P-value? (Round to four decimal places as​ needed.)

What is the conclusion about the null​ hypothesis?

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

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

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

D. 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 warrant rejection of the claim that 24​% of offspring peas will be yellow.

B. There is not sufficient evidence to support the claim that less than 24​% of offspring peas will be yellow.

C. There is not sufficient evidence to warrant rejection of the claim that 24​% of offspring peas will be yellow.

D. There is sufficient evidence to support the claim that less than 24​% 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

n = 416

x = 165

= x / n = 165 / 416 = 0.3966

P₀ = 0.27

1 - P₀ = 1 - 0.27 = 0.73

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.3966 - 0.27 / [(0.27 * 0.73) / 416]

= 5.818

Test statistic = 5.82

P(z > 5.82) = 1 - P(z < 5.82) = 1 - 1 = 0

P-value = 2 * 0 = 0

= 0.01

P-value <

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

A. There is sufficient evidence to warrant rejection of the claim that 24​% of offspring peas will be yellow.