Consider the following random sample of diameter measurements (in inches) of 17 Softballs. 4.79, 4.85, 4.23, 4.16, 4.68, 4.87, 4.84, 4.87, 4.7, 4.89 4.89, 4.81, 4.74, 4.77, 4.68, 4.76, 4.69 If we assume that the diameter measureme are normally distributed, find a 90% confidence interval for the mean diameter of a soft ball Give the lower limit and upper limit of the 90% confidence interval, Lower limit= Upper limit= Carry your intermediate Computations to at least three decimal Places. Round your answers to two decimal places.
Consider the following random sample of diameter measurements (in inches) of 17 Softballs. 4.79, 4.85, 4.23, 4.16, 4.68, 4.87, 4.84, 4.87, 4.7, 4.89 4.89, 4.81, 4.74, 4.77, 4.68, 4.76, 4.69 If we assume that the diameter measureme are normally distributed, find a 90% confidence interval for the mean diameter of a soft ball Give the lower limit and upper limit of the 90% confidence interval, Lower limit= Upper limit= Carry your intermediate Computations to at least three decimal Places. Round your answers to two decimal places.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Exploring Confidence Intervals for Softball Diameter Measurements
Welcome to our educational section on understanding confidence intervals through a practical example involving the diameter measurements of softballs.
#### Problem Statement
Consider the following random sample of diameter measurements (in inches) of 17 softballs:
```
4.79, 4.85, 4.73, 4.76, 4.68, 4.87, 4.84, 4.87, 4.7, 4.89, 4.81, 4.74, 4.77, 4.68, 4.76, 4.69
```
#### Goal
Assuming that the diameter measurements are normally distributed, we aim to find a 90% confidence interval for the mean diameter of a softball. For this calculation, we will:
1. Determine the **lower limit** and **upper limit** of the 90% confidence interval.
2. Carry intermediate computations to at least three decimal places.
3. Round the final answers to two decimal places.
**Instructions:**
1. Calculate the sample mean ( \(\bar{x}\) ).
2. Calculate the sample standard deviation ( \(s\) ).
3. Determine the t-score for the 90% confidence level and sample size ( degrees of freedom = n-1 ).
4. Calculate the margin of error ( \(E\) ).
5. Find the lower and upper limits of the confidence interval.
#### Formulae
- **Sample Mean (\(\bar{x}\))**: Sum of all sample observations divided by the number of observations.
\[
\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i
\]
- **Sample Standard Deviation (\(s\))**:
\[
s = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}}
\]
- **Margin of Error (E)**:
\[
E = t_{\alpha/2} \left( \frac{s}{\sqrt{n}} \right)
\]
Where \( t_{\alpha/2} \) is the t-score corresponding to the 90% confidence level and \( n-1 \) degrees of freedom.
- **Confidence Interval**:
\[
\text{Lower Limit} = \bar{x} - E
\]
\[
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Transcribed Image Text:### Exploring Confidence Intervals for Softball Diameter Measurements
Welcome to our educational section on understanding confidence intervals through a practical example involving the diameter measurements of softballs.
#### Problem Statement
Consider the following random sample of diameter measurements (in inches) of 17 softballs:
```
4.79, 4.85, 4.73, 4.76, 4.68, 4.87, 4.84, 4.87, 4.7, 4.89, 4.81, 4.74, 4.77, 4.68, 4.76, 4.69
```
#### Goal
Assuming that the diameter measurements are normally distributed, we aim to find a 90% confidence interval for the mean diameter of a softball. For this calculation, we will:
1. Determine the **lower limit** and **upper limit** of the 90% confidence interval.
2. Carry intermediate computations to at least three decimal places.
3. Round the final answers to two decimal places.
**Instructions:**
1. Calculate the sample mean ( \(\bar{x}\) ).
2. Calculate the sample standard deviation ( \(s\) ).
3. Determine the t-score for the 90% confidence level and sample size ( degrees of freedom = n-1 ).
4. Calculate the margin of error ( \(E\) ).
5. Find the lower and upper limits of the confidence interval.
#### Formulae
- **Sample Mean (\(\bar{x}\))**: Sum of all sample observations divided by the number of observations.
\[
\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i
\]
- **Sample Standard Deviation (\(s\))**:
\[
s = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}}
\]
- **Margin of Error (E)**:
\[
E = t_{\alpha/2} \left( \frac{s}{\sqrt{n}} \right)
\]
Where \( t_{\alpha/2} \) is the t-score corresponding to the 90% confidence level and \( n-1 \) degrees of freedom.
- **Confidence Interval**:
\[
\text{Lower Limit} = \bar{x} - E
\]
\[
\
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