A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 738hours. A random sample of 26 light bulbs has a mean life of 711 hours. Assume the population is normally distributed and the population standard deviation is 55 hours. At α=0.02, 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≠738(claim) Ha: μ=738 B. H0: μ≤711 Ha: μ>711 (claim) C. H0: μ=711 Ha: μ≠711 (claim) D. H0: μ<711 (claim) Ha: μ≥711 E. H0: μ≥738 (claim) Ha: μ<738 F. H0: μ>738 Ha: μ≤738 (claim) (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). PICTURE ATTACHED Choose the correct answer below. (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. Reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 738 hours. B. Fail to reject H0. There is not sufficient evidence to reject the claim that mean bulb life is at least 738 hours. C. Fail to reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 738 hours. D. Reject H0. There is not sufficient evidence to reject the claim that mean bulb life is at least 738 hours.

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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A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 738hours. A random sample of 26
light bulbs has a mean life of 711 hours. Assume the population is normally distributed and the population standard deviation is 55 hours. At α=0.02,
do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e).

(a) Identify the null hypothesis and alternative hypothesis.

H0:

μ≠738(claim)

Ha:

μ=738

H0:

μ≤711

Ha:

μ>711

(claim)

H0:

μ=711

Ha:

μ≠711

(claim)

H0:

μ<711

(claim)

Ha:

μ≥711

H0:

μ≥738

(claim)

Ha:

μ<738

H0:

μ>738

Ha:

μ≤738

(claim)

(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).

PICTURE ATTACHED

Choose the correct answer below.

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.

Reject

H0.

There

sufficient evidence to reject the claim that mean bulb life is at least

738

hours.

Fail to reject

H0.

There

is not

sufficient evidence to reject the claim that mean bulb life is at least

738

hours.

Fail to reject

H0.

There

sufficient evidence to reject the claim that mean bulb life is at least

738

hours.

Reject

H0.

There

is not

sufficient evidence to reject the claim that mean bulb life is at least

738

hours.

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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