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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## Estimating Mean Repair Costs for Vehicle Collisions

### Sample Data Overview

Your company self-insures its fleet of cars against collisions. To appropriately allocate funds for potential repairs, you need to estimate the mean repair costs per accident. Below is a dataset of repair costs ($) derived from a random sample of accidents:

```
1320, 1370, 2155, 1965, 2595, 2345, 1870, 2760
2125, 2185, 1970, 1075, 1950, 1920, 1305, 2320
2305, 2095, 965, 1455, 2645, 2790
1655, 2025, 2020, 1830, 1990, 2170, 2370, 2055
1485, 2095, 2650, 2285, 1840, 1940, 1670
1590, 2690, 1860, 2135, 1720, 1640
```

### Analysis Questions

#### Question 19
**Estimate of the Mean Repair Cost**

- Possible answers:
  - a. $2,274
  - b. $2,179
  - c. $2,087
  - d. $1,999

#### Question 20
**Standard Deviation of the Sample Data**

- Possible answers:
  - a. $484.52
  - b. $464.10
  - c. $444.54
  - d. $425.80

#### Question 21
**Margin of Error for an Interval Estimate with a 95% Confidence Level**

- Possible answers:
  - a. $129.08 

### Discussion

To accurately manage financial reserves for collision repairs, understanding statistical measures like the mean and standard deviation is crucial. The mean provides insight into average repair costs, while the standard deviation reveals the variability in costs. The margin of error, particularly with a 95% confidence level, helps in determining the reliability of the estimated mean.

This hands-on exercise not only aids in financial planning but also enhances statistical analysis skills by interpreting real-world data.
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Transcribed Image Text:## Estimating Mean Repair Costs for Vehicle Collisions ### Sample Data Overview Your company self-insures its fleet of cars against collisions. To appropriately allocate funds for potential repairs, you need to estimate the mean repair costs per accident. Below is a dataset of repair costs ($) derived from a random sample of accidents: ``` 1320, 1370, 2155, 1965, 2595, 2345, 1870, 2760 2125, 2185, 1970, 1075, 1950, 1920, 1305, 2320 2305, 2095, 965, 1455, 2645, 2790 1655, 2025, 2020, 1830, 1990, 2170, 2370, 2055 1485, 2095, 2650, 2285, 1840, 1940, 1670 1590, 2690, 1860, 2135, 1720, 1640 ``` ### Analysis Questions #### Question 19 **Estimate of the Mean Repair Cost** - Possible answers: - a. $2,274 - b. $2,179 - c. $2,087 - d. $1,999 #### Question 20 **Standard Deviation of the Sample Data** - Possible answers: - a. $484.52 - b. $464.10 - c. $444.54 - d. $425.80 #### Question 21 **Margin of Error for an Interval Estimate with a 95% Confidence Level** - Possible answers: - a. $129.08 ### Discussion To accurately manage financial reserves for collision repairs, understanding statistical measures like the mean and standard deviation is crucial. The mean provides insight into average repair costs, while the standard deviation reveals the variability in costs. The margin of error, particularly with a 95% confidence level, helps in determining the reliability of the estimated mean. This hands-on exercise not only aids in financial planning but also enhances statistical analysis skills by interpreting real-world data.
### Mathematical Concepts on Interval Estimates and Sample Data Analysis

#### Standard Deviation of Sample Data
To determine the standard deviation of a sample data set, the available options are:

a) $484.52  
b) $464.10  
c) $444.54  
d) $425.80  

#### Margin of Error with 95% Confidence Level
Calculating the margin of error for an interval estimate at a 95% confidence level, the potential values are:

a) $129.08  
b) $134.46  
c) $140.06  
d) $145.90  

#### Minimum Sample Size Calculation
To achieve a margin of error of $65 with a 95% confidence level, using standard deviation from the sample data as a guiding value, calculate the minimum sample size necessary. The choices are:

a) 131  
b) 142  
c) 162  
d) 180  

#### Alternative Interval Estimate of Mean Repair Cost
An alternative interval estimate of the mean repair cost, using the same sample size as the original, resulted in a 95% confidence interval of:

$1,884.91 to $2,122.59

The sample standard deviation for this interval can be:

a) $425.81  
b) $417.46  
c) $409.27  
d) $401.25  

#### Additional Instructions
Use the binary data in the worksheet tab labeled "LWP" to answer further questions, specifically Questions 24-28. 

This exercise demonstrates how statistical measures such as standard deviation, margin of error, and sample size are crucial for making informed decisions based on data analysis.
expand button
Transcribed Image Text:### Mathematical Concepts on Interval Estimates and Sample Data Analysis #### Standard Deviation of Sample Data To determine the standard deviation of a sample data set, the available options are: a) $484.52 b) $464.10 c) $444.54 d) $425.80 #### Margin of Error with 95% Confidence Level Calculating the margin of error for an interval estimate at a 95% confidence level, the potential values are: a) $129.08 b) $134.46 c) $140.06 d) $145.90 #### Minimum Sample Size Calculation To achieve a margin of error of $65 with a 95% confidence level, using standard deviation from the sample data as a guiding value, calculate the minimum sample size necessary. The choices are: a) 131 b) 142 c) 162 d) 180 #### Alternative Interval Estimate of Mean Repair Cost An alternative interval estimate of the mean repair cost, using the same sample size as the original, resulted in a 95% confidence interval of: $1,884.91 to $2,122.59 The sample standard deviation for this interval can be: a) $425.81 b) $417.46 c) $409.27 d) $401.25 #### Additional Instructions Use the binary data in the worksheet tab labeled "LWP" to answer further questions, specifically Questions 24-28. This exercise demonstrates how statistical measures such as standard deviation, margin of error, and sample size are crucial for making informed decisions based on data analysis.
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