A random sample of 860 births in a state included 429 boys. Construct a 95% confidence interval estimate of the proportion of boys in all births. It is believed that among all births, the proportion of boys is 0.509. Do these sample results provide strong evidence against that belief? .... Construct a 95% confidence interval estimate of the proportion of boys in all births.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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**Problem Statement:**

A random sample of 860 births in a state included 429 boys. Construct a 95% confidence interval estimate of the proportion of boys in all births. It is believed that among all births, the proportion of boys is 0.509. Do these sample results provide strong evidence against that belief?

**Task:**

Construct a 95% confidence interval estimate of the proportion of boys in all births.

\[ \_\_ < p < \_\_ \]  
*(Round to three decimal places as needed.)*

**Question:**

Do these sample results provide strong evidence against that belief?

**Options:**

- **A.** There is not strong evidence against 0.509 as the value of the proportion of boys in all births because 0.509 is contained within the 95% confidence interval.
  
- **B.** There is strong evidence against 0.509 as the value of the proportion of boys in all births because 0.509 is not contained within the 95% confidence interval.
  
- **C.** There is not strong evidence against 0.509 as the value of the proportion of boys in all births because 0.509 is not contained within the 95% confidence interval.
  
- **D.** There is strong evidence against 0.509 as the value of the proportion of boys in all births because 0.509 is contained within the 95% confidence interval.

**Usage:**

This exercise is useful for understanding confidence interval construction and interpretation in the context of hypothesis testing regarding population proportions.
Transcribed Image Text:**Problem Statement:** A random sample of 860 births in a state included 429 boys. Construct a 95% confidence interval estimate of the proportion of boys in all births. It is believed that among all births, the proportion of boys is 0.509. Do these sample results provide strong evidence against that belief? **Task:** Construct a 95% confidence interval estimate of the proportion of boys in all births. \[ \_\_ < p < \_\_ \] *(Round to three decimal places as needed.)* **Question:** Do these sample results provide strong evidence against that belief? **Options:** - **A.** There is not strong evidence against 0.509 as the value of the proportion of boys in all births because 0.509 is contained within the 95% confidence interval. - **B.** There is strong evidence against 0.509 as the value of the proportion of boys in all births because 0.509 is not contained within the 95% confidence interval. - **C.** There is not strong evidence against 0.509 as the value of the proportion of boys in all births because 0.509 is not contained within the 95% confidence interval. - **D.** There is strong evidence against 0.509 as the value of the proportion of boys in all births because 0.509 is contained within the 95% confidence interval. **Usage:** This exercise is useful for understanding confidence interval construction and interpretation in the context of hypothesis testing regarding population proportions.
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