### MATH110 Problem Set 04#### Problem 2Use the given data to find the minimum sample size required to estimate the population proportion.(a) **Parameters:**- Margin of Error: 0.04- Confidence Level: 95%- Estimated Proportion ($\hat{p}$): 0.64(b) **Parameters:**- Margin of Error: 0.006- Confidence Level: 95%- Estimated Proportion ($\hat{p}$) and Complement ($\hat{q}$) are unknown#### Problem 3Use the given degree of confidence and sample data to construct a confidence interval for the population mean $\mu$. Assume that the population has a normal distribution. **MATH110 Problem Set 04**1) Construct a confidence interval for the population proportion $ p $.- $ n = 144 $- $ x = 86 $- 90% confidence**Explanation:**This problem asks you to construct a confidence interval for the population proportion $ p $. Given:- $ n = 144 $: the sample size.- $ x = 86 $: the number of successes in the sample.- A confidence level of 90%.To solve this, you will calculate the sample proportion $ \hat{p} = \frac{x}{n} $ and use the standard error to construct the confidence interval. The formula for a confidence interval at a 90% confidence level is:\[ \hat{p} \pm Z \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \]where $ Z $ is the Z-score corresponding to the desired confidence level.

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2) Use the given data to find the minimum sample size required to estimate the population proportion. (a) Margin of error: 0.04, confidence level: 95%, p = 0.64 (b) Margin of error: 0.006, confidence level: 95%, § and ĝ are unknown

2) Use the given data to find the minimum sample size required to estimate the population proportion. (a) Margin of error: 0.04, confidence level: 95%, p = 0.64 (b) Margin of error: 0.006, confidence level: 95%, § and ĝ are unknown

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Concept explainers

2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.

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Question

### MATH110 Problem Set 04

#### Problem 2

Use the given data to find the minimum sample size required to estimate the population proportion.

(a) **Parameters:**
- Margin of Error: 0.04
- Confidence Level: 95%
- Estimated Proportion ($\hat{p}$): 0.64

(b) **Parameters:**
- Margin of Error: 0.006
- Confidence Level: 95%
- Estimated Proportion ($\hat{p}$) and Complement ($\hat{q}$) are unknown

#### Problem 3

Use the given degree of confidence and sample data to construct a confidence interval for the population mean $\mu$. Assume that the population has a normal distribution.

**MATH110 Problem Set 04**

1) Construct a confidence interval for the population proportion $ p $.

- $ n = 144 $
- $ x = 86 $
- 90% confidence

**Explanation:**

This problem asks you to construct a confidence interval for the population proportion $ p $. Given:

- $ n = 144 $: the sample size.
- $ x = 86 $: the number of successes in the sample.
- A confidence level of 90%.

To solve this, you will calculate the sample proportion $ \hat{p} = \frac{x}{n} $ and use the standard error to construct the confidence interval. The formula for a confidence interval at a 90% confidence level is:

\[ \hat{p} \pm Z \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \]

where $ Z $ is the Z-score corresponding to the desired confidence level.

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