MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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# Calculate the Standard Error and Assess Normality 

## Instructions
- **Calculate the standard error**: You will calculate the standard error for each set of values given.
- **Assess normality**: Determine if normality may be assumed. 
- **Round your answers to 4 decimal places**.

## Data Table

### Parameters:
- **n**: sample size
- **π**: population proportion

| ( ) |   | Standard Error | Normality |
|-----|---|----------------|-----------|
| **(a)** | \( n = 30, \; \pi = .60 \) |  | Yes |
| **(b)** | \( n = 58, \; \pi = .57 \) |  | Yes |
| **(c)** | \( n = 110, \; \pi = .59 \) |  | Yes |
| **(d)** | \( n = 550, \; \pi = .006 \) |  | No |

## Explanation
- **Standard Error**: To be calculated and filled in.
- **Normality**: Indicates whether the assumption of normality can be made based on the sample size and proportion given.

### Notes:
1. Use the formula for the standard error of the proportion:
\[
SE = \sqrt{\frac{\pi(1 - \pi)}{n}}
\]
2. For normality, generally, if both \( n\pi \) and \( n(1-\pi) \) are greater than 5, normality can be assumed. 

**Students are required to fill in the Standard Error column with the calculated values.**
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Transcribed Image Text:# Calculate the Standard Error and Assess Normality ## Instructions - **Calculate the standard error**: You will calculate the standard error for each set of values given. - **Assess normality**: Determine if normality may be assumed. - **Round your answers to 4 decimal places**. ## Data Table ### Parameters: - **n**: sample size - **π**: population proportion | ( ) | | Standard Error | Normality | |-----|---|----------------|-----------| | **(a)** | \( n = 30, \; \pi = .60 \) | | Yes | | **(b)** | \( n = 58, \; \pi = .57 \) | | Yes | | **(c)** | \( n = 110, \; \pi = .59 \) | | Yes | | **(d)** | \( n = 550, \; \pi = .006 \) | | No | ## Explanation - **Standard Error**: To be calculated and filled in. - **Normality**: Indicates whether the assumption of normality can be made based on the sample size and proportion given. ### Notes: 1. Use the formula for the standard error of the proportion: \[ SE = \sqrt{\frac{\pi(1 - \pi)}{n}} \] 2. For normality, generally, if both \( n\pi \) and \( n(1-\pi) \) are greater than 5, normality can be assumed. **Students are required to fill in the Standard Error column with the calculated values.**
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