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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Question

A car battery manufacturer claims that its car batteries last at least 4 years on average, under normal operating conditions. However, many consumers have experienced battery failure well before 4 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 74 batteries was collected and tested by the consumer advocacy group and the mean lifespan was found to be 3.95 years.

Use the critical value method to test the hypothesis that the mean lifespan of this brand of car battery is less than 4 years, using α=0.005. Assume that the standard deviation of the lifespans of all batteries produced by this company is known to be 0.65 year.

Left-tailed

The standard normal (zz) 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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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