Answered: Based on these data, can the consumer…

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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$**Educational Website Content: Hypothesis Testing** **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?** To answer this question, we need to perform a hypothesis test regarding $ \mu_d $ (the population mean difference in tread wear for the two brands of tires). It is assumed that this population of differences (Brand 1 minus Brand 2) is normally distributed. We will perform a two-tailed test. Complete the following steps, rounding intermediate computations to three or more decimal places and final answers as specified. Use a list of formulas if necessary. ### (a) State the Hypotheses - Null Hypothesis $ H_0 $: [ ] - Alternative Hypothesis $ H_1 $: [ ] ### (b) Determine the Type of Test Statistic - Type of test statistic: [Choose one from the dropdown] ### (c) Find the Value of the Test Statistic - Test statistic value: [ ] ### (d) Find the Critical Values at the 0.10 Level of Significance - Critical values: [ ] and [ ] ### (e) Conclusion Can the consumer group conclude that the mean tread wears of the brands differ at the 0.10 level of significance? - [ ] Yes - [ ] No **Explanation and Analysis** Each part guides the user through conducting a hypothesis test. The interface requires users to select appropriate hypotheses, determine the correct statistical test, calculate the test statistic, determine critical values, and reach a conclusion based on the level of significance and the computed statistics. This structured methodology ensures a comprehensive approach to hypothesis testing, fostering a deeper understanding and application of statistical principles.$

Transcribed Image Text:**Educational Website Content: Hypothesis Testing** **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?** To answer this question, we need to perform a hypothesis test regarding $ \mu_d $ (the population mean difference in tread wear for the two brands of tires). It is assumed that this population of differences (Brand 1 minus Brand 2) is normally distributed. We will perform a two-tailed test. Complete the following steps, rounding intermediate computations to three or more decimal places and final answers as specified. Use a list of formulas if necessary. ### (a) State the Hypotheses - Null Hypothesis $ H_0 $: [ ] - Alternative Hypothesis $ H_1 $: [ ] ### (b) Determine the Type of Test Statistic - Type of test statistic: [Choose one from the dropdown] ### (c) Find the Value of the Test Statistic - Test statistic value: [ ] ### (d) Find the Critical Values at the 0.10 Level of Significance - Critical values: [ ] and [ ] ### (e) Conclusion Can the consumer group conclude that the mean tread wears of the brands differ at the 0.10 level of significance? - [ ] Yes - [ ] No **Explanation and Analysis** Each part guides the user through conducting a hypothesis test. The interface requires users to select appropriate hypotheses, determine the correct statistical test, calculate the test statistic, determine critical values, and reach a conclusion based on the level of significance and the computed statistics. This structured methodology ensures a comprehensive approach to hypothesis testing, fostering a deeper understanding and application of statistical principles.

$### Tire Tread Wear Analysis A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary significantly depending on the type of car, so the group attempts to eliminate this variable by installing the two brands on the same 8 cars, chosen at random. Specifically, 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 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. #### Tread Wear Data (in inches) | Car | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |-------------|------|------|------|------|------|------|------|------| | **Brand 1** | 0.50 | 0.54 | 0.40 | 0.50 | 0.53 | 0.40 | 0.54 | 0.42 | | **Brand 2** | 0.40 | 0.28 | 0.41 | 0.27 | 0.41 | 0.30 | 0.41 | 0.28 | | **Difference (Brand 1 - Brand 2)** | 0.10 | 0.26 | -0.01 | 0.23 | 0.12 | 0.10 | 0.13 | 0.14 | ### Statistical Analysis 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? They can answer this question by performing a hypothesis test regarding $ \mu_d $, 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. 1. **Two-Tailed Test:** - Complete the following steps, rounding intermediate computations to three or more decimal places, and round your final answers as specified. 2. **Hypotheses:** - **(a)** State the null hypothesis $ H_0 $ and$

Transcribed Image Text:### Tire Tread Wear Analysis A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary significantly depending on the type of car, so the group attempts to eliminate this variable by installing the two brands on the same 8 cars, chosen at random. Specifically, 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 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. #### Tread Wear Data (in inches) | Car | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |-------------|------|------|------|------|------|------|------|------| | **Brand 1** | 0.50 | 0.54 | 0.40 | 0.50 | 0.53 | 0.40 | 0.54 | 0.42 | | **Brand 2** | 0.40 | 0.28 | 0.41 | 0.27 | 0.41 | 0.30 | 0.41 | 0.28 | | **Difference (Brand 1 - Brand 2)** | 0.10 | 0.26 | -0.01 | 0.23 | 0.12 | 0.10 | 0.13 | 0.14 | ### Statistical Analysis 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? They can answer this question by performing a hypothesis test regarding $ \mu_d $, 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. 1. **Two-Tailed Test:** - Complete the following steps, rounding intermediate computations to three or more decimal places, and round your final answers as specified. 2. **Hypotheses:** - **(a)** State the null hypothesis $ H_0 $ and

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