Question

genetic experiment involving peas yielded one sample of offspring consisting of 422 green peas and 134...

genetic experiment involving peas yielded one sample of offspring consisting of

422

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.

To Test :-

H0 :- P = 0.24
H1 :- P ≠ 0.24

P = X / n = 134/556 = 0.241

Test Statistic :-
Z = ( P - P0 ) / ( √((P0 * q0)/n)
Z = ( 0.241 - 0.24 ) / ( √(( 0.24 * 0.76) /556))
Z = 0.0556

Test Criteria :-
Reject null hypothesis if Z > Z(α/2)
Z(α/2) = Z(0.01/2) = 2.576
Z < Z(α/2) = 0.0556 < 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 > 0.0556 )  = 0.9557
Reject null hypothesis if P value < α = 0.01
Since P value = 0.9557 > 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 24​% of offspring peas is yellow.

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