9 20 21 Questions 19-22 are related to the following 22 Your company self-insures its fleet of cars against collisions. You need to estimate the mean repair costs per accident so 23 that you can set aside enough money to cover these costs. The data for repair cost for a random sample of accidents is 24 shown below. 25 26 27 28 29 30 31 32 d $104,905 34 a 35 b 36 с d 78 37 33 19 The point estimate of the mean repair cost is, $2,274 $2,179 $2,087 $1,999 242 C 243 d 244 245 21 246 a 1320 2125 Ready 2305 1655 1540 1485 $484.52 $464.10 $444.54 $425.80 238 239 20 The standard deviation of the sample data is, 240 a 241 b 1370 2185 2950 2025 2005 2305 2155 1970 2050 2020 1990 1590 E270 HW5 LWP WEED Accessibility: Investigate Type here to search 1965 1075 2095 1830 2650 2690 2595 1950 965 1990 2285 1860 The margin of error for an interval estimate with a 95% level of confidence is, $129.08 2345 1920 1455 2170 O E 1840 2135 1870 1305 2645 2370 1940 1720 2760 2320 2790 2055 1670 1640 L Ⓡ

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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.
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.
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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