Testing a Claim about a Proportion

Question

A genetic experiment involving peas yielded one sample of offspring consisting of 427427 green peas and 167167 yellow peas. Use a 0.05 significance level to test the claim that under the same​ circumstances, 2626​% 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.

The test statistic for this hypothesis test is ______.

​(Round to two decimal places as​ needed.)

Identify the​ P-value for this hypothesis test.

The​ P-value for this hypothesis test is _______.

Answer 1

Let p_o be the observed proportion of offspring peas being yellow. Let p-hat be the estimated proportion of offspring peas being yellow.

H_o: p_o = 0.26

H_a: p_o ≠ 0.26

p-hat = 167/(167 + 427) = 167/594 = 0.2811

z = 0.2811 - 0.26 / √[(0.2811)(0.7189)/594] = 0.0211/0.01845 = 1.14

P(z ≤ 1.14) = 0.8729

P(z > 1.14) = 1 - 0.8729 = 0.1271

Since z = 1.14 < 1.96 and the p-value = 0.1271 > 0.05, we fail to reject the null hypothesis. There is no sufficient evidence to show that 26% of the offspring peas will be yellow.