Answered: Students in a business statistics…

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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Question

Please find the test statistic the critical value is there sufficient evidence in the mean strength of the four brands of trash bags

Transcribed Image Text:**Weight Required to Break Trash Bags** The table below displays the weight (in pounds) needed to break trash bags of four different brands. This test is designed to compare the strength and durability of the trash bags across various brands. | | Brand 1 | Brand 2 | Brand 3 | Brand 4 | |------|---------|---------|---------|---------| | **1** | 32 | 35 | 34 | 21 | | **2** | 40 | 36 | 37 | 20 | | **3** | 35 | 37 | 39 | 17 | | **4** | 31 | 43 | 34 | 19 | | **5** | 37 | 36 | 33 | 20 | | **6** | 33 | 34 | 34 | 22 | This data is crucial for understanding which brand offers the best resistance to weight stress before breaking, assisting consumers in making informed choices based on durability.

Transcribed Image Text:**Randomized Design Analysis on Trash Bag Strength** *Study Background:* Students in a business statistics course conducted an experiment to assess the strength of four different brands of trash bags. This was achieved by incrementally placing one-pound weights into each bag until it ruptured. The experiment included a total of 24 bags, with 6 bags tested from each brand. The accompanying data table (not shown here) details the weight in pounds necessary to break each of the trash bags. *Statistical Analysis Plan:* 1. **Data Access:** - Access the data table via the provided icon. - View a partial table of critical values of F. - View a partial table of critical values for the Studentized Range, Q. 2. **Hypothesis Testing:** - At the 0.05 significance level, determine if there is a notable difference in the mean strength among the four brands of trash bags. 3. **Hypothesis Options:** - **Option A:** - Null Hypothesis (H₀): μ₁ = μ₂ = ... = μ₆ - Alternative Hypothesis (H₁): Not all μⱼ are equal (j = 1, 2, ... , 6) - **Option B (Correct Answer):** - Null Hypothesis (H₀): μ₁ = μ₂ = ... = μ₄ - Alternative Hypothesis (H₁): Not all μⱼ are equal (j = 1, 2, 3, 4) - **Option C:** - Null Hypothesis (H₀): μ₁ = μ₂ = ... = μ₄ - Alternative Hypothesis (H₁): μ₁ ≠ μ₂ ≠ ... ≠ μ₄ - **Option D:** - Null Hypothesis (H₀): μ₁ = μ₂ = ... = μ₆ - Alternative Hypothesis (H₁): μ₁ ≠ μ₂ ≠ ... ≠ μ₆ 4. **Statistical Calculation:** - Calculate the test statistic (F_STAT) and round to two decimal places as necessary. *Note:* The study aims to utilize these statistical tests to conclude whether there is a statistically significant difference in the performance of the trash bag brands under study.

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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