Question

a genetic experiment involving peas yielded one sample of offspring consisting of 438 green peas and 120 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.

z = - 1.38
(round to two decimal places as needed.)
what is the p - value?
p - value = 0.168
(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 less than or equal to the significance level, α.
b. fail to reject the null hypothesis because the p - value is greater than the significance level, α.
c. fail to reject the null hypothesis because the p - value is less than or equal to the significance level, α.
d. reject the null hypothesis because the p - value is greater than the significance level, α.

Explanation:

Step1: Compare P - value and significance level

We are given a significance level \(\alpha = 0.01\) and a P - value \(P=0.168\).

Step2: Make a decision

Since \(P = 0.168>0.01=\alpha\)

Answer:

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