Question

a genetic experiment involving peas yielded one sample of offspring consisting of 439 green peas and 171 yellow peas. use a 0.01 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.

what is the p - value?
p - value = 0.252
(round to three decimal places as needed.)

what is the conclusion about the null hypothesis?
a. reject the null hypothesis because the p - value is greater than the significance level, α.
b. reject the null hypothesis because the p - value is less than or equal to the significance level, α.
c. fail to 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 less than or equal to the significance level, α.

Explanation:

Step1: Recall the decision rule for P - value method

If \(P - value\leq\alpha\), reject \(H_0\). If \(P - value>\alpha\), fail to reject \(H_0\). Here \(\alpha = 0.01\) and \(P - value=0.252\)

Step2: Compare P - value and significance level

Since \(0.252>0.01\) (i.e., \(P - value>\alpha\))

Answer:

C. Fail to reject the null hypothesis because the P - value is greater than the significance level, \(\alpha\).