Question

A genetic experiment involving peas yielded one sample of offspring consisting of 418 green peas and 158 yellow peas. Use a 0.05 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. Upper H 0 : p not equals 0.26 Upper H 1 : p equals 0.26 B. Upper H 0 : p equals 0.26 Upper H 1 : p not equals 0.26 C. Upper H 0 : p not equals 0.26 Upper H 1 : p less than 0.26 D. Upper H 0 : p not equals 0.26 Upper H 1 : p greater than 0.26 E. Upper H 0 : p equals 0.26 Upper H 1 : p less than 0.26 F. Upper H 0 : p equals 0.26 Upper H 1 : p greater than 0.26

What is the test statistic? z= (Round to two decimal places as needed.)

What is the P-value? P-value = (Round to four decimal places as needed.)

What is the conclusion about the null hypothesis?

A. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, alpha.

B. Fail to reject the null hypothesis because the P-value is greater than the significance level, alpha.

C. Reject the null hypothesis because the P-value is greater than the significance level, alpha.

D. Reject the null hypothesis because the P-value is less than or equal to the significance level, alpha.

What is the final conclusion?

A. There is sufficient evidence to warrant rejection of the claim that 26 % of offspring peas will be yellow.

B. There is not sufficient evidence to support the claim that less than 26 % of offspring peas will be yellow.

C. There is not sufficient evidence to warrant rejection of the claim that 26 % of offspring peas will be yellow.

D. There is sufficient evidence to support the claim that less than 26 % of offspring peas will be yellow. Click to select your answer(s).

Answer 1

Solution :

Given that,

= 0.26

1 - = 0.74

n =418

x = 158

Level of significance = = 0.05

Point estimate = sample proportion = = x / n = 158 / 418 = 0.378

This a left tailed test.

C)

Ho: p = 0.26

Ha: p < 0.26

Test statistics

z = ( - ) / *(1-) / n

= ( 0.378 - 0.26) / (0.26*0.74) / 418

= 5.50

P-value

= P(Z <z )

= P(Z < 5.50)

= 1.0000

The p-value is p = 1, and since p = 1 >0.05, it is concluded that the null hypothesis is fails to reject.

B) Fail to reject the null hypothesis because the P-value is greater than the significance level, alpha.

Conclusion:

B) There is not sufficient evidence to support the claim that less than 26 % of offspring peas will be yellow.