Question

A genetic experiment involving peas yielded one sample of offspring consisting of 448 green peas and 127 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.

Answer 1

null Hypothesis:               Ho:		p	=	0.2700
alternate Hypothesis:    Ha:		p	≠	0.2700
for 0.1 level with two tailed test , critical value of z=			1.6449
Decision rule :                   reject Ho if absolute value of test statistic |z|>1.645
sample success                                                           x                    =				127
sample size		n                    =		575
std error       =Se		=√(p*(1-p)/n) =		0.0185
sample proportion     p̂		x/n=		0.2209
test stat = z                =		(p̂-p)/Se=		-2.6536
p value		=		0.0080

as p value is less than 0.05 level of significance we reject null hypothesis

we have sufficient evidence to conclude that  offspring peas that will be yellow is different from 27%.