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.

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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.
**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.
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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