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

Question

A genetic experiment involving peas yielded one sample of offspring consisting of 415 green peas and 126 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.

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

b. what is the p-value? p-value = ?? ( round to four decimal places)

c. what is the conclusion about the null hypothesis?

(a)reject the null hypothesis because p-value is greater than the significance level, a.

(b) fail to reject the null hypothesis because the p-value is greater than the significance level, a.

(c) reject the null hypothesis because the p value is less than or egqual to the signifiance level, a.

(d) fail to reject the null hypothesis because the p-value is less than or equal to the significance level, a.

d. what is the final conclusion?

(a) there is not sufficient evidence to warrant rejection of the claim that 27% of offspring peas will be yellow

(b) there is sufficient evidence to support the claim that less than 27% of offspring peas will be yellow

(c) there is sufficent evidence to warrent rejection of the claim that 27% of offspring peas will be yellow

(d) there is not sufficient evidence to support the claim that less than 27% of offspring peas will be yellow

Explanation / Answer

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.27
HA : p 0.27

Hypothesis test results:

Hence,

a) Test statistic = -1.94

b) p - Value = 0.0519

c) Conclusion: Fail to reject the null hypothesis because the p-value is greater than the significance level, a.

Option B is correct.

d) Final conclusion: There is not sufficient evidence to warrant rejection of the claim that 27% of offspring peas will be yellow.

Option A is correct.

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