Question

A genetic experiment involving peas yielded one sample of offspring consisting of 432 green peas and 121 yellow peas. Use a 0.05 significance level to test the claim that under the same​ circumstances, 27​% 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. Upper H 0 : p not equals 0.27 Upper H 1 : p greater than 0.27 B. Upper H 0 : p equals 0.27 Upper H 1 : p less than 0.27 C. Upper H 0 : p equals 0.27 Upper H 1 : p not equals 0.27 Your answer is correct.D. Upper H 0 : p not equals 0.27 Upper H 1 : p equals 0.27 E. Upper H 0 : p not equals 0.27 Upper H 1 : p less than 0.27 F. Upper H 0 : p equals 0.27 Upper H 1 : p greater than 0.27 What is the test​ statistic? zequals nothing ​(Round to two decimal places as​ needed.)

Answer 1

The Hypotheses are:

Rejection region:

Reject Ho if |Z| > Z _0.025=1.96

Test Statistic is calculated as

P-value:

P-value is computed using Z score and Z table shown below hence P-value=0.0251

Conclusion:

Since the |Z|> Z _0.025 and P-value< 0.05 hence we reject the null hypothesis and conclude that there is enough evidence to support the claim.