Answered: At the 0.05 level of significance, is…

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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The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,543 hours. The population standard deviation is

1,080 hours. A random sample of 81 light bulbs indicates a sample means a life of 7,243 hours.

a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,543 hours?

b. Compute the test statistic and critical value

c. Construct a 95%confidence interval estimate of the population mean a life of the light bulbs.

d. Compare the results of (a) and (c). What conclusions do you reach?

a. Let μ be the population mean. Determine the null hypothesis,

H0, and the alternative hypothesis, H1.

H0: μ=__

H1: μ≠__

b. What is the test statistic and Z critical value?

ZSTAT=__

(Round to two decimal places as needed.)

What is/are the critical value(s)?

____

(Round to two decimal places as needed. Use a comma to separate answers as needed.)

What is the final conclusion?

A. Fail to reject H0. There is not sufficient evidence to prove that the mean life is different from 7,543 hours.

B. Fail to reject H0. There is sufficient evidence to prove that the mean life is different from 7,543 hours.

C. Reject H0. There is sufficient evidence to prove that the mean life is different from 7,543 hours.

D. Reject H0. There is not sufficient evidence to prove that the mean life is different from 7,543 hours.

c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs.

__ ≤μ≤ __

(Round to one decimal place as needed.)

d. Compare the results of (a) and (c). What conclusions do you reach?

A.The results of (a) and (c) are not the same: there is sufficient evidence to prove that the mean life is different from 7,543 hours.

B. The results of (a) and (c) are the same: there is not sufficient evidence to prove that the mean life is different from 7,543 hours.

C. The results of (a) and (c) are the same: there is sufficient evidence to prove that the mean life is different from 7,543 hours.

D. The results of (a) and (c) are not the same: there is not sufficient evidence to prove that the mean life is different from 7,543 hours.

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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