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 are the null and alternative hypotheses?

a. $h_0:p = 0.26$
$h_1:p
eq0.26$

b. $h_0:p
eq0.26$
$h_1:p = 0.26$

c. $h_0:p
eq0.26$
$h_1:p>0.26$

d. $h_0:p
eq0.26$
$h_1:p<0.26$

e. $h_0:p = 0.26$
$h_1:p<0.26$

f. $h_0:p = 0.26$
$h_1:p>0.26$

Explanation:

Step1: Understand the claim

The claim is that \(26\%\) of offspring peas will be yellow. In hypothesis testing, the null hypothesis \(H_0\) is a statement of equality. The alternative hypothesis \(H_1\) is the statement that we are trying to find evidence for.

Step2: Analyze each option

• Option A: \(H_0: p = 0.26\) (null hypothesis is equality, which is correct as it represents the claim value) and \(H_1: p

eq0.26\) (alternative hypothesis for a two - tailed test. Since the problem just tests the claim that \(p = 0.26\) without specifying a direction (more or less), a two - tailed test is appropriate).

• Option B: \(H_0: p

eq0.26\) is incorrect because the null hypothesis should be the statement of equality.

• Option C: \(H_0: p

eq0.26\) is wrong (null should be equality) and \(H_1: p > 0.26\) is a one - tailed test which is not indicated by the problem.

• Option D: \(H_0: p

eq0.26\) is wrong (null should be equality) and \(H_1: p < 0.26\) is a one - tailed test which is not indicated by the problem.

• Option E: \(H_1: p < 0.26\) is a one - tailed test which is not indicated by the problem.
• Option F: \(H_1: p > 0.26\) is a one - tailed test which is not indicated by the problem.

Answer:

A. \(H_0: p = 0.26\), \(H_1: p
eq0.26\)