A genetic experiment involving peas yielded one sample of offspring consisting of 442 green peas and 142 yellow peas. Use a 0.01 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.
A genetic experiment involving peas yielded one sample of offspring consisting of 442 green peas and 142 yellow peas. Use a 0.01 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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![A genetic experiment involving peas yielded one sample of offspring consisting of 442 green peas and 142 yellow peas. Use a 0.01 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.
**What are the null and alternative hypotheses?**
- A. \( H_0: p = 0.24 \)
\( H_1: p > 0.24 \)
- B. \( H_0: p \neq 0.24 \)
\( H_1: p = 0.24 \)
- C. \( H_0: p \neq 0.24 \)
\( H_1: p > 0.24 \)
- D. \( H_0: p = 0.24 \)
\( H_1: p < 0.24 \)
- E. \( H_0: p = 0.24 \)
\( H_1: p \neq 0.24 \)
- F. \( H_0: p \neq 0.24 \)
\( H_1: p < 0.24 \)
**What is the test statistic?**
\[ z = \square \]
(Round to two decimal places as needed.)
**What is the P-value?**
P-value = \(\square\)
(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 greater than the significance level, \( \alpha \).
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Transcribed Image Text:A genetic experiment involving peas yielded one sample of offspring consisting of 442 green peas and 142 yellow peas. Use a 0.01 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.
**What are the null and alternative hypotheses?**
- A. \( H_0: p = 0.24 \)
\( H_1: p > 0.24 \)
- B. \( H_0: p \neq 0.24 \)
\( H_1: p = 0.24 \)
- C. \( H_0: p \neq 0.24 \)
\( H_1: p > 0.24 \)
- D. \( H_0: p = 0.24 \)
\( H_1: p < 0.24 \)
- E. \( H_0: p = 0.24 \)
\( H_1: p \neq 0.24 \)
- F. \( H_0: p \neq 0.24 \)
\( H_1: p < 0.24 \)
**What is the test statistic?**
\[ z = \square \]
(Round to two decimal places as needed.)
**What is the P-value?**
P-value = \(\square\)
(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 greater than the significance level, \( \alpha \).
**Interaction:**
To continue with the next steps, please click the "Next" button.

Transcribed Image Text:**What is the conclusion about the null hypothesis?**
- **A.** Fail to reject the null hypothesis because the P-value is greater than the significance level, α.
- **B.** Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, α.
- **C.** Reject the null hypothesis because the P-value is less than or equal to the significance level, α.
- **D.** Reject the null hypothesis because the P-value is greater than the significance level, α.
**What is the final conclusion?**
- **A.** There is sufficient evidence to support the claim that less than 24% of offspring peas will be yellow.
- **B.** There is sufficient evidence to warrant rejection of the claim that 24% of offspring peas will be yellow.
- **C.** There is not sufficient evidence to support the claim that less than 24% of offspring peas will be yellow.
- **D.** There is not sufficient evidence to warrant rejection of the claim that 24% of offspring peas will be yellow.
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It is given that a sample of offspring consisting of 442 green peas in which 142 are yellow peas.
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