Find the minimum sample size n needed to estimate u for the given values of c, o, and E. c = 0.90, o = 9.8, and E = 1 Assume that a preliminary sample has at least 30 members. n = (Round up to the nearest whole number.)
Find the minimum sample size n needed to estimate u for the given values of c, o, and E. c = 0.90, o = 9.8, and E = 1 Assume that a preliminary sample has at least 30 members. n = (Round up to the nearest whole number.)
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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![### Determining Sample Size
#### Problem Description:
Find the minimum sample size \( n \) needed to estimate \( \mu \) for the given values of \( c \), \( \sigma \), and \( E \).
Given values:
- \( c = 0.90 \)
- \( \sigma = 9.8 \)
- \( E = 1 \)
#### Additional Information:
Assume that a preliminary sample has at least 30 members.
#### Task:
Compute the value of \( n \) using the provided parameters and round up to the nearest whole number.
#### Solution:
To solve this, apply the sample size formula for estimating the mean with a given confidence level:
\[ n = \left( \frac{Z_{\alpha/2} \cdot \sigma}{E} \right)^2 \]
Where:
- \( Z_{\alpha/2} \) is the critical value of the standard normal distribution corresponding to the desired confidence level \( c \).
- \( \sigma \) is the population standard deviation.
- \( E \) is the margin of error.
By calculating the critical value and inserting the known values into the formula, you can determine \( n \). Be sure to round the resulting value to the nearest whole number as specified.
**To proceed with the specific calculation:**
1. Determine the critical value \( Z_{\alpha/2} \) for \( c = 0.90 \).
2. Substitute these values into the formula.
3. Calculate and round the final value of \( n \).
This process yields the required sample size necessary to estimate the population mean \( \mu \) within the specified margin of error \( E \) at the given confidence level \( c \) and standard deviation \( \sigma \).
Please, fill in the required calculations and determine the value for \( n \).
**Interactive Component:**
\[ n = \boxed{} \]
(Round up to the nearest whole number.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf5b27fc-182c-458d-bf52-a3d5fb8d4e7e%2F3d1bc4bb-8f6a-4015-9836-c7526378cc2d%2F87c6i4_processed.png&w=3840&q=75)
Transcribed Image Text:### Determining Sample Size
#### Problem Description:
Find the minimum sample size \( n \) needed to estimate \( \mu \) for the given values of \( c \), \( \sigma \), and \( E \).
Given values:
- \( c = 0.90 \)
- \( \sigma = 9.8 \)
- \( E = 1 \)
#### Additional Information:
Assume that a preliminary sample has at least 30 members.
#### Task:
Compute the value of \( n \) using the provided parameters and round up to the nearest whole number.
#### Solution:
To solve this, apply the sample size formula for estimating the mean with a given confidence level:
\[ n = \left( \frac{Z_{\alpha/2} \cdot \sigma}{E} \right)^2 \]
Where:
- \( Z_{\alpha/2} \) is the critical value of the standard normal distribution corresponding to the desired confidence level \( c \).
- \( \sigma \) is the population standard deviation.
- \( E \) is the margin of error.
By calculating the critical value and inserting the known values into the formula, you can determine \( n \). Be sure to round the resulting value to the nearest whole number as specified.
**To proceed with the specific calculation:**
1. Determine the critical value \( Z_{\alpha/2} \) for \( c = 0.90 \).
2. Substitute these values into the formula.
3. Calculate and round the final value of \( n \).
This process yields the required sample size necessary to estimate the population mean \( \mu \) within the specified margin of error \( E \) at the given confidence level \( c \) and standard deviation \( \sigma \).
Please, fill in the required calculations and determine the value for \( n \).
**Interactive Component:**
\[ n = \boxed{} \]
(Round up to the nearest whole number.)
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