Use the following to answer the next 3 questions. A lumber manufacturing company would like to compare the average weight capacity of two types of boards they currently manufacture. The sampled boards were obtained using a random mechanism. 350 300 250 Weight in lbs for Board A vs Board B Board A Board B Population Board A Board B Sample mean 305.4 lbs 331.7 lbs Sample Standard Sample deviation Size 36.5 44.3 data: boardA and boardB t = -2.0875, df = 36, p-value = 0.0439 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -51.8601685 -0.7621273 sample estimates: mean of x mean of y 305.3603 331.6715 16 26 22. Describe the side-by-side boxplot. Include a comparison of the two groups, the center, shape and spread of each.
Use the following to answer the next 3 questions. A lumber manufacturing company would like to compare the average weight capacity of two types of boards they currently manufacture. The sampled boards were obtained using a random mechanism. 350 300 250 Weight in lbs for Board A vs Board B Board A Board B Population Board A Board B Sample mean 305.4 lbs 331.7 lbs Sample Standard Sample deviation Size 36.5 44.3 data: boardA and boardB t = -2.0875, df = 36, p-value = 0.0439 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -51.8601685 -0.7621273 sample estimates: mean of x mean of y 305.3603 331.6715 16 26 22. Describe the side-by-side boxplot. Include a comparison of the two groups, the center, shape and spread of each.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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### Summary Statistics
The following table presents the sample mean, sample standard deviation, and sample size for both Board A and Board B:
| Population | Sample Mean | Sample Standard Deviation | Sample Size |
|------------|--------------|--------------------------|-------------|
| Board A | 305.4 lbs | 36.5 | 16 |
| Board B | 331.7 lbs | 44.3 | 26 |
### Statistical Analysis
A hypothesis test was conducted to determine if there is a significant difference between the means of Board A and Board B.
The results are as follows:
- t-statistic: -2.0875
- Degrees of freedom (df): 36
- p-value: 0.0439
- 95% Confidence Interval for the difference in means: [-51.8601685, -0.7621273]
The sample estimates for the mean of each group:
- Mean of Board A: 305.3603 lbs
- Mean of Board B: 331.6715 lbs
### Interpretation of Boxplots
#### Center
The median weight of Board B is higher than the median weight of Board A, indicating that, on average, Board B has a higher weight capacity.
#### Spread
Board B exhibits a larger spread in weight capacity values compared to Board A. This is reflected in Board B’s larger interquartile range (IQR) and total range.
#### Shape
Both boxplots show symmetry around their medians, with no notable skewness. The whiskers extend more in Board B, suggesting a higher variability.
#### Outliers
Both boxes represent the middle 50% of the data while whiskers represent the variability outside the middle 50%. There are no apparent outliers.
### Conclusion
The statistical test supports the alternative hypothesis that there is a significant difference in the average weight capacities between](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1420db0a-b432-4e35-a393-1b1ae00a8fe8%2F5dd5d612-bfbe-439d-b2b7-81499b0c4ca5%2Fwpcxzec_processed.png&w=3840&q=75)
Transcribed Image Text:**Statistical Analysis of Weight Capacity Between Board A and Board B**
### Background
A lumber manufacturing company aims to compare the average weight capacity (in pounds) between two types of boards they currently manufacture, referred to as Board A and Board B. The analysis involves data obtained from randomly sampled boards.
### Boxplots
The boxplots below illustrate the distribution of weight capacities for Board A and Board B. Each boxplot summarizes data using the median, quartiles, and potential outliers.
### Summary Statistics
The following table presents the sample mean, sample standard deviation, and sample size for both Board A and Board B:
| Population | Sample Mean | Sample Standard Deviation | Sample Size |
|------------|--------------|--------------------------|-------------|
| Board A | 305.4 lbs | 36.5 | 16 |
| Board B | 331.7 lbs | 44.3 | 26 |
### Statistical Analysis
A hypothesis test was conducted to determine if there is a significant difference between the means of Board A and Board B.
The results are as follows:
- t-statistic: -2.0875
- Degrees of freedom (df): 36
- p-value: 0.0439
- 95% Confidence Interval for the difference in means: [-51.8601685, -0.7621273]
The sample estimates for the mean of each group:
- Mean of Board A: 305.3603 lbs
- Mean of Board B: 331.6715 lbs
### Interpretation of Boxplots
#### Center
The median weight of Board B is higher than the median weight of Board A, indicating that, on average, Board B has a higher weight capacity.
#### Spread
Board B exhibits a larger spread in weight capacity values compared to Board A. This is reflected in Board B’s larger interquartile range (IQR) and total range.
#### Shape
Both boxplots show symmetry around their medians, with no notable skewness. The whiskers extend more in Board B, suggesting a higher variability.
#### Outliers
Both boxes represent the middle 50% of the data while whiskers represent the variability outside the middle 50%. There are no apparent outliers.
### Conclusion
The statistical test supports the alternative hypothesis that there is a significant difference in the average weight capacities between
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