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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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