### Testing Battery Lifespan ClaimsA car battery manufacturer claims that its car batteries last at least 5 years on average, under normal operating conditions. However, many consumers have experienced battery failure well before 5 years. A consumer advocacy group decided to investigate the company to determine if the company's claim about the average lifespan of their car batteries is exaggerated and misleading.A random sample of 51 batteries was collected and tested by the consumer advocacy group, and the mean lifespan was found to be 4.89 years.Use the critical value method to test the hypothesis that the mean lifespan of this brand of car battery is less than 5 years, using a significance level of 5%. Assume that the standard deviation of the lifespans of all batteries produced by this company is known to be 0.38 years.#### State the null and alternative hypothesis for this test.\[ H_0: \mu \ge 5 \]\[ H_1: \mu < 5 \]#### Determine if this test is left-tailed, right-tailed, or two-tailed.- Two-tailed- Right-tailed- **Left-tailed** (Correct Answer)#### Should the standard normal (z) distribution or Student's (t) distribution be used for this test?- The Student's t distribution should be used.- **The standard normal (z) distribution should be used** (Correct Answer since population standard deviation is known and sample size is large).---### Explanation of Graphs and DiagramsThere are no graphs or diagrams present in the question text provided. The task mainly focuses on formulating and testing a hypothesis regarding the mean lifespan of the car batteries using statistical methods such as the critical value method. ### Hypothesis Testing Exercise**Choose the appropriate distribution for the hypothesis test:**- [ ] The Student's t distribution should be used- [ ] The standard normal (z) distribution should be used**Determine the critical value(s) for this hypothesis test. Round the solution(s) to two decimal places. If more than one critical value exists, enter the solutions using a comma-separated list.**[____________________]**Determine the test statistic. Round the solution to two decimal places.**[____________________]**Determine the appropriate conclusion for this hypothesis test:**- [ ] The sample data do not provide sufficient evidence to reject the alternative hypothesis that the mean lifespan of batteries produced by this company is less than 5 years and thus we conclude that the company's claim that the batteries last at least 5 years is likely false.- [ ] The sample data provide sufficient evidence to reject the alternative hypothesis that the mean lifespan of batteries produced by this company is less than 5 years and thus we conclude that the company's claim that the batteries last at least 5 years is likely true.- [ ] The sample data provide sufficient evidence to reject the null hypothesis that the mean lifespan of batteries produced by this company is at least 5 years and thus we conclude that the company's claim that the batteries last at least 5 years is likely false.- [ ] The sample data do not provide sufficient evidence to reject the null hypothesis that the mean lifespan of batteries produced by this company is at least 5 years and thus we conclude that the company's claim that the batteries last at least 5 years is likely true.**Note:**Be sure to use statistical methods to make your determination. This exercise involves calculating critical values and test statistics to appropriately reject or fail to reject the null or alternative hypotheses.

Given, sample size (n) = 51 sample mean (x̄) = 4.89 standard deviation (σ) = 0.38 population mean…

Answered: A car battery manufacturer claims that…

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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$### Testing Battery Lifespan Claims A car battery manufacturer claims that its car batteries last at least 5 years on average, under normal operating conditions. However, many consumers have experienced battery failure well before 5 years. A consumer advocacy group decided to investigate the company to determine if the company's claim about the average lifespan of their car batteries is exaggerated and misleading. A random sample of 51 batteries was collected and tested by the consumer advocacy group, and the mean lifespan was found to be 4.89 years. Use the critical value method to test the hypothesis that the mean lifespan of this brand of car battery is less than 5 years, using a significance level of 5%. Assume that the standard deviation of the lifespans of all batteries produced by this company is known to be 0.38 years. #### State the null and alternative hypothesis for this test. \[ H_0: \mu \ge 5 \] \[ H_1: \mu < 5 \] #### Determine if this test is left-tailed, right-tailed, or two-tailed. - Two-tailed - Right-tailed - **Left-tailed** (Correct Answer) #### Should the standard normal (z) distribution or Student's (t) distribution be used for this test? - The Student's t distribution should be used. - **The standard normal (z) distribution should be used** (Correct Answer since population standard deviation is known and sample size is large). --- ### Explanation of Graphs and Diagrams There are no graphs or diagrams present in the question text provided. The task mainly focuses on formulating and testing a hypothesis regarding the mean lifespan of the car batteries using statistical methods such as the critical value method.$

Transcribed Image Text:### Testing Battery Lifespan Claims A car battery manufacturer claims that its car batteries last at least 5 years on average, under normal operating conditions. However, many consumers have experienced battery failure well before 5 years. A consumer advocacy group decided to investigate the company to determine if the company's claim about the average lifespan of their car batteries is exaggerated and misleading. A random sample of 51 batteries was collected and tested by the consumer advocacy group, and the mean lifespan was found to be 4.89 years. Use the critical value method to test the hypothesis that the mean lifespan of this brand of car battery is less than 5 years, using a significance level of 5%. Assume that the standard deviation of the lifespans of all batteries produced by this company is known to be 0.38 years. #### State the null and alternative hypothesis for this test. \[ H_0: \mu \ge 5 \] \[ H_1: \mu < 5 \] #### Determine if this test is left-tailed, right-tailed, or two-tailed. - Two-tailed - Right-tailed - **Left-tailed** (Correct Answer) #### Should the standard normal (z) distribution or Student's (t) distribution be used for this test? - The Student's t distribution should be used. - **The standard normal (z) distribution should be used** (Correct Answer since population standard deviation is known and sample size is large). --- ### Explanation of Graphs and Diagrams There are no graphs or diagrams present in the question text provided. The task mainly focuses on formulating and testing a hypothesis regarding the mean lifespan of the car batteries using statistical methods such as the critical value method.

### Hypothesis Testing Exercise

**Choose the appropriate distribution for the hypothesis test:**

- [ ] The Student's t distribution should be used
- [ ] The standard normal (z) distribution should be used

**Determine the critical value(s) for this hypothesis test. Round the solution(s) to two decimal places. If more than one critical value exists, enter the solutions using a comma-separated list.**

[____________________]

**Determine the test statistic. Round the solution to two decimal places.**

[____________________]

**Determine the appropriate conclusion for this hypothesis test:**

- [ ] The sample data do not provide sufficient evidence to reject the alternative hypothesis that the mean lifespan of batteries produced by this company is less than 5 years and thus we conclude that the company's claim that the batteries last at least 5 years is likely false.

- [ ] The sample data provide sufficient evidence to reject the alternative hypothesis that the mean lifespan of batteries produced by this company is less than 5 years and thus we conclude that the company's claim that the batteries last at least 5 years is likely true.

- [ ] The sample data provide sufficient evidence to reject the null hypothesis that the mean lifespan of batteries produced by this company is at least 5 years and thus we conclude that the company's claim that the batteries last at least 5 years is likely false.

- [ ] The sample data do not provide sufficient evidence to reject the null hypothesis that the mean lifespan of batteries produced by this company is at least 5 years and thus we conclude that the company's claim that the batteries last at least 5 years is likely true.

**Note:**
Be sure to use statistical methods to make your determination. This exercise involves calculating critical values and test statistics to appropriately reject or fail to reject the null or alternative hypotheses.

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