A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 775 hours. A random sample of 20 light bulbs has a mean life of 760 hours. Assume the population is normally distributed and the population standard deviation is 58 hours. At α=0.08, do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e). A. Identify the null hypothesis and alternative hypothesis. A.H0:μ=760 Ha:μ≠760(claim) B.H0:μ≥775(claim) Ha:μ<775 C.H0:μ≤760 Ha:μ>760(claim) D.H0:μ>775 Ha:μ≤775(claim) E.H0:μ<760(claim) Ha:μ≥760 F.H0:μ≠775(claim) Ha:μ= (b) Identify the critical value(s). Use technology. z0=_(Use a comma to separate answers as needed. Round to two decimal places as needed.) Identify the rejection region(s). (c) Identify the standardized test statistic. Use technology. z= _______(Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. A. Fail to reject H0. There is not sufficient evidence to reject the claim that mean bulb life is at least 775 hours. B. Reject H0. There is not sufficient evidence to reject the claim that mean bulb life is at least 775 hours. C. Reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 775 hours. D. Fail to reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 775 hours.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 775

hours. A random sample of 20 light bulbs has a mean life of 760 hours. Assume the population is normally distributed and the population standard deviation is 58 hours. At α=0.08, do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e).

A. Identify the null hypothesis and alternative hypothesis.

A.H0:μ=760
Ha:μ≠760(claim)

B.H0:μ≥775(claim)
Ha:μ<775

C.H0:μ≤760
Ha:μ>760(claim)

D.H0:μ>775

Ha:μ≤775(claim)

E.H0:μ<760(claim)

Ha:μ≥760

F.H0:μ≠775(claim)

Ha:μ=

(b) Identify the critical value(s). Use technology.

z0=_____(Use a comma to separate answers as needed. Round to two decimal places as needed.)

Identify the rejection region(s).

(c) Identify the standardized test statistic. Use technology.

z= ___________(Round to two decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

A. Fail to reject H0. There is not sufficient evidence to reject the claim that mean bulb life is at least 775 hours.

B. Reject H0. There is not sufficient evidence to reject the claim that mean bulb life is at least 775 hours.

C. Reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 775 hours.

D. Fail to reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 775 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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