Question

A genetic experiment involving peas yielded one sample of offspring consisting of 405 green peas and 156

yellow peas. Use a 0.05 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 is the final conclusion?

A.There is not 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 warrant rejection of the claim that 27​% of offspring peas will be yellow.

Answer 1

null​ hypothesis,Ho:p=0.27

alternative​ hypothesis,Ha p 0.27

alpha=0.05

test statistic is

z=p^-p/sqrt(p*(1-p)/n

sample proportion,p^=x/n=156/405=0.3851852

z=(0.3851852-0.27)/sqrt(0.27*(1-0.27)/405)

z=5.221327

P=0.0000

p<0.05

Reject Ho,

Accept Ha.

there is no sufficient statistical evidence at 5% level of significance to conclude that  under the same​ circumstances, 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.