Question

a genetic experiment involving peas yielded one sample of offspring consisting of 420 green peas and 156 yellow peas. use a 0.05 significance level to test the claim that under the same circumstances, 25% 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 = 0.25 ) ( h_1:p
eq0.25 )
○b. ( h_0:p
eq0.25 ) ( h_1:p = 0.25 )
○c. ( h_0:p
eq0.25 ) ( h_1:plt0.25 )
○d. ( h_0:p = 0.25 ) ( h_1:plt0.25 )
○e. ( h_0:p
eq0.25 ) ( h_1:pgt0.25 )
○f. ( h_0:p = 0.25 ) ( h_1:pgt0.25 )

Explanation:

Step1: Understand the claim

The claim is about the proportion of yellow peas. The null hypothesis \(H_0\) is a statement of equality. The alternative hypothesis \(H_1\) is the claim we are testing against the null. Since the claim is “25% of offspring peas will be yellow” (a non - directional claim, just a proportion value), the null hypothesis is \(H_0:p = 0.25\) and the alternative hypothesis is \(H_1:p
eq0.25\) (a two - tailed test).

Step2: Analyze the options

• Option A: \(H_0:p = 0.25\) and \(H_1:p

eq0.25\) is correct for a two - tailed test about the proportion \(p = 0.25\).

• Option B: The null hypothesis \(H_0:p

eq0.25\) is incorrect because the null hypothesis should be a statement of equality for proportion tests.

• Option C: \(H_0:p

eq0.25\) is wrong (null should be equality) and \(H_1:p < 0.25\) is a one - tailed test which is not appropriate for the non - directional claim.

• Option D: \(H_1:p < 0.25\) is a one - tailed test which is not appropriate for the non - directional claim.
• Option E: \(H_0:p

eq0.25\) is wrong (null should be equality) and \(H_1:p>0.25\) is a one - tailed test which is not appropriate for the non - directional claim.

• Option F: \(H_1:p>0.25\) is a one - tailed test which is not appropriate for the non - directional claim.

Answer:

A. \(H_0:p = 0.25\), \(H_1:p
eq0.25\)