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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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please answer part b Also is there significant evidence that brand 1 and 3 different in mean ratings? is there significant evidence that brand 1 and 4 different in mean ratings? is there significant evidence that brand 2 and 3 different in mean ratings? is there significant evidence that brand 2 and 4 different in mean ratings? is there significant evidence that brand 3 and 4 different in mean ratings?

Transcribed Image Text:**Title: Comparative Strength Analysis of Four Brands of Trash Bags** **Introduction:** In a controlled experiment conducted by a statistics course, the strength of four different brands of trash bags was tested. Each brand's ability to withstand weight before breaking was measured in pounds. A completely randomized design was used, and a total of 24 trash bags (6 per brand) were evaluated. The results are detailed in the table below. **Table: Weight (in pounds) Required to Break the Trash Bags** | | Brand 1 | Brand 2 | Brand 3 | Brand 4 | |--------|---------|---------|---------|---------| | **Bag 1** | 34 | 34 | 37 | 18 | | **Bag 2** | 39 | 36 | 34 | 17 | | **Bag 3** | 35 | 37 | 37 | 20 | | **Bag 4** | 34 | 36 | 35 | 19 | | **Bag 5** | 36 | 38 | 36 | 20 | | **Bag 6** | 37 | 34 | 34 | 17 | **Explanation:** The table presents the weight in pounds needed to cause each brand's trash bags to break. Each column represents a different brand, and each row within the column indicates the result for an individual bag from that brand. - **Brand 1** had weights ranging from 34 to 39 pounds. - **Brand 2** had weights between 34 and 38 pounds. - **Brand 3** resisted weights from 34 to 37 pounds. - **Brand 4** showed the least resistance, with weights from 17 to 20 pounds. **Conclusion:** This data provides insights into the durability of each brand's trash bags, highlighting significant differences in their strength. This experiment is crucial for consumers looking to purchase trash bags that meet their specific needs for durability. Further statistical analysis can identify which brand offers the most reliable performance based on average breaking weight.

$**Experiment Summary** Students in a business statistics course performed a completely randomized design to test the strength of four brands of trash bags. One-pound weights were placed into a bag, one at a time, until the bag broke. A total of 24 bags, 6 for each brand, were used. The data provide the weight (in pounds) required to break the trash bags. These steps were followed: 1. **View Data Table**: Access the full data table of results. 2. **View Critical Values (F)**: Access a partial table of critical values for F-statistic. 3. **View Critical Values (Studentized Range, Q)**: Access the critical values for Studentized Range. **Statistical Analysis** - **Test Statistic**: $ F_{\text{STAT}} = 172.07 $ (Rounded to two decimal places as needed.) - **Critical Value**: $ F_{\alpha} = 3.10 $ (Rounded to two decimal places as needed.) **Conclusion** - **Decision**: Reject $ H_0 $. There is sufficient evidence of a difference in the mean strength of the four brands of trash bags. **Further Analysis** b. **Determine Which Brands Differ in Mean Ratings** Assess if there is significant evidence that Brand 1 and Brand 2 differ in mean strength. - **Options**: - A. Yes - B. No - C. It is not appropriate to test which brands differ in mean strength.$

Transcribed Image Text:**Experiment Summary** Students in a business statistics course performed a completely randomized design to test the strength of four brands of trash bags. One-pound weights were placed into a bag, one at a time, until the bag broke. A total of 24 bags, 6 for each brand, were used. The data provide the weight (in pounds) required to break the trash bags. These steps were followed: 1. **View Data Table**: Access the full data table of results. 2. **View Critical Values (F)**: Access a partial table of critical values for F-statistic. 3. **View Critical Values (Studentized Range, Q)**: Access the critical values for Studentized Range. **Statistical Analysis** - **Test Statistic**: $ F_{\text{STAT}} = 172.07 $ (Rounded to two decimal places as needed.) - **Critical Value**: $ F_{\alpha} = 3.10 $ (Rounded to two decimal places as needed.) **Conclusion** - **Decision**: Reject $ H_0 $. There is sufficient evidence of a difference in the mean strength of the four brands of trash bags. **Further Analysis** b. **Determine Which Brands Differ in Mean Ratings** Assess if there is significant evidence that Brand 1 and Brand 2 differ in mean strength. - **Options**: - A. Yes - B. No - C. It is not appropriate to test which brands differ in mean strength.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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