Answered: The manufacturer of a particular brand…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

$### Statistical Hypothesis Testing for Tire Lifespan Claims The manufacturer of a particular brand of tires claims they average at least 50,000 miles before needing to be replaced. From past studies of this tire, it is known that the population standard deviation is 8,000 miles. A survey of tire owners was conducted. From the 30 tires surveyed, the mean lifespan was 43,500 miles. Using alpha = 0.05, can we prove that the data is inconsistent with the manufacturers' claim? We should use a **?** test. #### What are the correct hypotheses? \[ H_0: \text{Select an answer} \ \ ? \] \[ H_a: \text{Select an answer} \ \ ? \] #### Based on the hypotheses, find the following: (Round test statistic and p-value to 4 decimal places.) Test Statistic = \[ \underline{\hspace{3cm}} \] p-value = \[ \underline{\hspace{3cm}} \] The correct decision is to \[ \text{Select an answer:} \ \ \underline{\hspace{3cm}} \] The correct conclusion would be: \[ \text{Select an answer:} \ \ \underline{\hspace{3cm}} \] **Instructions for Completion:** 1. Determine whether to use a z-test or t-test based on the given information. 2. State the null hypothesis $H_0$ and the alternative hypothesis $H_a$. Typically this involves comparing the sample mean to the claimed population mean of 50,000 miles. 3. Calculate the test statistic. 4. Determine the p-value associated with the test statistic. 5. Make a decision based on the p-value and the significance level ($\alpha = 0.05$). 6. Draw the correct conclusion based on the decision. This exercise is designed to guide students through the process of hypothesis testing, using a real-world example related to tire lifespan claims by a manufacturer. It covers essential steps, including hypothesis formulation, test selection, calculation, decision-making, and conclusion drawing.$

Transcribed Image Text:### Statistical Hypothesis Testing for Tire Lifespan Claims The manufacturer of a particular brand of tires claims they average at least 50,000 miles before needing to be replaced. From past studies of this tire, it is known that the population standard deviation is 8,000 miles. A survey of tire owners was conducted. From the 30 tires surveyed, the mean lifespan was 43,500 miles. Using alpha = 0.05, can we prove that the data is inconsistent with the manufacturers' claim? We should use a **?** test. #### What are the correct hypotheses? \[ H_0: \text{Select an answer} \ \ ? \] \[ H_a: \text{Select an answer} \ \ ? \] #### Based on the hypotheses, find the following: (Round test statistic and p-value to 4 decimal places.) Test Statistic = \[ \underline{\hspace{3cm}} \] p-value = \[ \underline{\hspace{3cm}} \] The correct decision is to \[ \text{Select an answer:} \ \ \underline{\hspace{3cm}} \] The correct conclusion would be: \[ \text{Select an answer:} \ \ \underline{\hspace{3cm}} \] **Instructions for Completion:** 1. Determine whether to use a z-test or t-test based on the given information. 2. State the null hypothesis $H_0$ and the alternative hypothesis $H_a$. Typically this involves comparing the sample mean to the claimed population mean of 50,000 miles. 3. Calculate the test statistic. 4. Determine the p-value associated with the test statistic. 5. Make a decision based on the p-value and the significance level ($\alpha = 0.05$). 6. Draw the correct conclusion based on the decision. This exercise is designed to guide students through the process of hypothesis testing, using a real-world example related to tire lifespan claims by a manufacturer. It covers essential steps, including hypothesis formulation, test selection, calculation, decision-making, and conclusion drawing.

Expert Solution

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Discrete Probability Distributions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions