Suppose a tire company developed two new brands of tires and would like to compare the variability of the tire life of the two. Both brands were driven under normal conditions, and random samples of the tires were collected. The table below shows th sizes and the standard deviations, in miles, calculated for each sample. Complete parts a and b. Brand 1 Brand 2 Sample standard deviation 3,700 miles 3,300 miles Sample size 30 30 a. Using a =0.10, determine if there is a difference in the variability of the two tire brands. Identify the null and alternative hypotheses. Họ: of (1). H, o (2). Calculate the appropriate test statistic. The test statistic is (Round to two decimal places as needed.) Determine the appropriate critical value(s). The critical value(s) is(are) (Round to three decimal places as needed. Use a comma to separate answers as needed.) (3)- the null hypothesis. There is (4). - evidence that the population variance for Brand 1 is (5) – the population variance for Brand 2. b. Use technology to find the p-value and interpret the result. The p-value is (Round to three decimal places as needed.) Since the p-value is (6). a= 0.10, (7). the null hypothesis. There is (8) evidence to conclude that the population variance for Brand 1 (9). Brand 2. (1) O = O 2 Os O Reject O Do not reject (4) O sufficient O insufficient O reject O do not reject (8) O insufficient O sufficient O equals O is less than is greater than O differs from (2) O O > (3) (5) O equal to O greater than O different from (6) O greater than O less than (7) (9) O less than

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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Transcribed Image Text:### Analysis of Tire Brand Variability Suppose a tire company developed two new brands of tires and aims to compare the variability of the tire life between the two. Both brands undergo testing under normal conditions, and random samples are collected. The table provides the sample sizes and standard deviations: | | Brand 1 | Brand 2 | |--------------------|---------|---------| | **Sample Standard Deviation** | 3,700 miles | 3,300 miles | | **Sample Size** | 30 | 30 | **Objective:** Determine if there is a statistical difference in the variability of the tire life between Brand 1 and Brand 2. --- ### Hypothesis Testing **a. Using α = 0.10** **Null and Alternative Hypotheses:** - **Null Hypothesis (H₀):** σ₁² (1) = σ₂² - **Alternative Hypothesis (H₁):** σ₁² (2) ≠ σ₂² **Test Statistic Calculation:** - **Test Statistic:** __________ (Round to two decimal places as needed.) **Critical Values Determination:** - **Critical Value(s):** __________ (Round to three decimal places as needed. Use a comma to separate answers as needed.) - (3) ___________ the null hypothesis. There is (4) ___________ evidence that the population variance for Brand 1 is (5) ___________ the population variance for Brand 2. **b. P-Value Calculation with Technology** - **P-Value:** __________ (Round to three decimal places as needed.) Since the p-value is (6) ___________ α = 0.10, (7) ___________ the null hypothesis. There is (8) ___________ evidence to conclude that the population variance for Brand 1 (9) ___________ Brand 2. --- **Options:** 1. (1) = ≠ ≤ < 2. (2) = ≠ ≤ < 3. Reject / Do not reject 4. Sufficient / Insufficient 5. Equal to / Greater than / Less than 6. Greater than / Less than 7. Reject / Do not reject 8. Insufficient / Sufficient 9. Equals / Is less than / Is greater than / Differs from ### Instructions Fill in the blanks and select the appropriate options to complete the hypothesis testing process

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