A genetic experiment involving peas yielded one sample of offspring consisting of 440 green peas and 145 yellow peas. Use a 0.05 significance level to test the claim that under the same circumstances, 26% 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.
H0: p = 0.26
H1: p < 0.26
What is the test statistic? (Round to two decimal places as needed.)
What is the P-value? (Round to four decimal places as needed.)
What is the conclusion about the null hypothesis?
A. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, α.
B. Reject the null hypothesis because the P-value is less than or equal to the significance level, α.
C. Reject the null hypothesis because the P-value is greater than the significance level, α.
D. Fail to reject the null hypothesis because the P-value is greater than the significance level, α.
What is the final conclusion?
A. There is sufficient evidence to support the claim that less than 26% of offspring peas will be yellow.
B. There is not sufficient evidence to warrant rejection of the claim that 26% of offspring peas will be yellow.
C. There is sufficient evidence to warrant rejection of the claim that 26% of offspring peas will be yellow.
D. There is not sufficient evidence to support the claim that less than 26% of offspring peas will be yellow.