Question

A genetic experiment involving peas yielded one sample of offspring consisting of 404 green peas and 134 yellow peas. Use a 0.01 significance level to test the claim that under the same​ circumstances, 24​% 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 test statistic?

Determine the P Value

Do we reject the null hypotheses or fail to reject

what is the final conclusion

Answer 1

To Test :-

H0 :- P = 0.24

H1 :- P 0.24

n = 538
P = X / n = 134 / 538 = 0.2491

Test Statistic :-


Z = 0.49

Test Criteria :-
Reject null hypothesis if

= 0.49 < 2.576, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = 2 * P ( Z > 0.49 )
P value = 0.6242
Reject null hypothesis if P value <
Since P value = 0.6242 > 0.01, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is sufficient evidence to support the claim that under the same​ circumstances, 24​% of offspring peas will be yellow at 0.01 significance level.