A genetic experiment involving peas yielded one sample of offspring consisting o

Question

A genetic experiment involving peas yielded one sample of offspring consisting of 412 green peas and 133 yellow peas. Use a 0.05 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.

Explanation / Answer

Samle Size n=412+133=545

Sample proportion of yellow p_hat=133/545=0.244

Null hypothesis H0: p=0.24=p0(say)

Alternative hypothesis H1:p Notequal 0.24

Test statistic Z= (p_hat-p0)/sqrt(p0*(1-p0)/n)

=(0.244-0.24)/sqrt(0.24*(1-0.24)/545)

=0.2186

p-value=P|Z|>0.2186)=2*P(Z<-0.2186)=0.8270

Asp-value>0.05,we do not reject the null hypothesis and conclude that the proportion of yellow offspring is not significantly different from 24% of the offspring

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