How to do it please show set by step ### Hypothesis Testing ExampleThis section guides you through the process of testing a hypothesis regarding mean tread wear for two different brands of tires using a two-sample test. Follow the steps below and complete the parts as instructed.1. **State the Hypotheses:** - **Null Hypothesis (\(H_0\))**: - **Alternative Hypothesis (\(H_1\))**:2. **Determine the Type of Test Statistic to Use:** - Choose the appropriate test statistic from the options provided.3. **Find the Value of the Test Statistic:** - Calculate the value of the test statistic. - Ensure to round your answer to three or more decimal places.4. **Find the Critical Values at the 0.10 Level of Significance:** - Identify the critical values needed for the test. - Provide the values, ensuring to round to three or more decimal places.5. **Conclusion at the 0.10 Level:** - Determine if the consumer group can conclude that the mean tread wears of the brands differ based on the test. - Choose either "Yes" or "No".### Diagram and Graph ExplanationOn the right side of the screen, a chart is displayed featuring several statistical symbols and notation options, including:- **μ (Mu)** - Population mean- **σ (Sigma)** - Population standard deviation- **ρ (Rho)** - Population proportion- **X̄ (X-bar)** - Sample mean- **S** - Sample standard deviation- **P̂ (P-hat)** - Sample proportionThese symbols and notations are essential for marking in your statistical calculations and hypothesis testing exercises.### Interactive Options- **Explanation Button**: Click this button for a detailed explanation of the solution steps.- **Check Button**: Use this to verify your answers.By following these steps and utilizing the options available, you can effectively conduct a hypothesis test to determine if there is a significant difference in the mean tread wears of the two brands of tires. ### Evaluation of Two Competing Brands of Tires: An Analysis of Tread WearA consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same 8 cars, chosen at random. Each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in the table below:| **Car** | **1** | **2** | **3** | **4** | **5** | **6** | **7** | **8** ||---------|-------|-------|-------|-------|-------|-------|-------|-------|| **Brand 1** | 0.40 | 0.46 | 0.53 | 0.54 | 0.37 | 0.30 | 0.47 | 0.45 || **Brand 2** | 0.35 | 0.53 | 0.54 | 0.50 | 0.36 | 0.28 | 0.48 | 0.47 || **Difference (Brand 1 - Brand 2)** | 0.05 | -0.07 | -0.01 | 0.04 | 0.01 | 0.02 | -0.01 | -0.02 |**Statistical Analysis Instructions**:Based on these data, can the consumer group conclude, at the 0.10 level of significance, that the mean tread wears of the brands differ? Answer this question by performing a hypothesis test regarding μ₄ (which is μ with a letter "d" subscript), the population mean difference in tread wear for the two brands of tires.Assume that this population of differences (Brand 1 minus Brand 2) is normally distributed.Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified.**Steps:**1. **State the Hypotheses**:

here given data of 8 car for brand 1 and brand 2 here performing two tail test for μd

Answered: (a) State the null hypothesis Ho and…

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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### Hypothesis Testing Example

This section guides you through the process of testing a hypothesis regarding mean tread wear for two different brands of tires using a two-sample test. Follow the steps below and complete the parts as instructed.

1. **State the Hypotheses:**
- **Null Hypothesis (\(H_0\))**:
- **Alternative Hypothesis (\(H_1\))**:

2. **Determine the Type of Test Statistic to Use:**
- Choose the appropriate test statistic from the options provided.

3. **Find the Value of the Test Statistic:**
- Calculate the value of the test statistic.
- Ensure to round your answer to three or more decimal places.

4. **Find the Critical Values at the 0.10 Level of Significance:**
- Identify the critical values needed for the test.
- Provide the values, ensuring to round to three or more decimal places.

5. **Conclusion at the 0.10 Level:**
- Determine if the consumer group can conclude that the mean tread wears of the brands differ based on the test.
- Choose either "Yes" or "No".

### Diagram and Graph Explanation

On the right side of the screen, a chart is displayed featuring several statistical symbols and notation options, including:

- **μ (Mu)** - Population mean
- **σ (Sigma)** - Population standard deviation
- **ρ (Rho)** - Population proportion
- **X̄ (X-bar)** - Sample mean
- **S** - Sample standard deviation
- **P̂ (P-hat)** - Sample proportion

These symbols and notations are essential for marking in your statistical calculations and hypothesis testing exercises.

### Interactive Options

- **Explanation Button**: Click this button for a detailed explanation of the solution steps.
- **Check Button**: Use this to verify your answers.

By following these steps and utilizing the options available, you can effectively conduct a hypothesis test to determine if there is a significant difference in the mean tread wears of the two brands of tires.

Transcribed Image Text:### Evaluation of Two Competing Brands of Tires: An Analysis of Tread Wear A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same 8 cars, chosen at random. Each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in the table below: | **Car** | **1** | **2** | **3** | **4** | **5** | **6** | **7** | **8** | |---------|-------|-------|-------|-------|-------|-------|-------|-------| | **Brand 1** | 0.40 | 0.46 | 0.53 | 0.54 | 0.37 | 0.30 | 0.47 | 0.45 | | **Brand 2** | 0.35 | 0.53 | 0.54 | 0.50 | 0.36 | 0.28 | 0.48 | 0.47 | | **Difference (Brand 1 - Brand 2)** | 0.05 | -0.07 | -0.01 | 0.04 | 0.01 | 0.02 | -0.01 | -0.02 | **Statistical Analysis Instructions**: Based on these data, can the consumer group conclude, at the 0.10 level of significance, that the mean tread wears of the brands differ? Answer this question by performing a hypothesis test regarding μ₄ (which is μ with a letter "d" subscript), the population mean difference in tread wear for the two brands of tires. Assume that this population of differences (Brand 1 minus Brand 2) is normally distributed. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. **Steps:** 1. **State the Hypotheses**:

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