Question

A genetic experiment involving peas yielded one sample of offspring consisting of

420

green peas and

134

yellow peas. Use a

0.05

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.

Answer 1

Let p be the true proportion of yellow offspring peas under the same​ circumstances. We want to test the claim that  under the same ​circumstances, 24% of offspring peas will be yellow. That is, we want to test the claim that p=0.24

The hypotheses are

From the sample we have the following

The hypothesized value of the proportion of yellow offspring is

The values

are both greater than 5. Hence we can use the normal distribution as an approximation to the binomial distribution as the sampling distribution of

The standard error of sample proportion is

The test statistic is

This is a 2 tailed test (The alternative hypothesis has "not equal to")

The p-value is the sum of area under both the tails

We will reject the null hypothesis, if the p-value is less than the significance level.

Here, the p-value is 0.9203 and it is greater than the significance level . Hence we do not reject the null hypothesis.

We conclude that there is no sufficient evidence to reject the claim that  under the same ​circumstances, 24% of offspring peas will be yellow.