A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 744 hours. A random sample of 30 light bulbs has a mean life of 732 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≥744 (claim) Ha: μ<744 B. H0: μ≠744(claim) Ha: μ=744 C. H0: μ=732 Ha: μ≠732 (claim) D. H0: μ<732 (claim) Ha: μ≥732 E. H0: μ≤732 Ha: μ>732 (claim) F. H0: μ>744 Ha: μ≤744 (claim) (b) Identify the critical value(s). Use technology. z0=nothing (Use a comma to separate answers as needed. Round to two decimal places as needed.) Identify the rejection region(s). Choose the correct answer below. A. -404z Reject H0. Fail to reject H0. A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at negative 2.1. The area under the curve to the left of negative 2.1 is shaded one color and labeled Reject Upper H 0. The area under the curve to the right of negative 2.1 is shaded another color and labeled Fail to reject Upper H 0. B. -404z Reject H0. Reject H0. Fail to reject H0. A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segments extend from the horizontal axis to the curve at negative 2.1 and 2.1. The area under the curve to the left of negative 2.1 is shaded and the area under the curve to the right of 2.1 are both shaded one color and labeled Reject Upper H 0.The area under the curve between negative 2.1 and 2.1 is shaded another color and labeled Fail to reject Upper H 0. C. -404z Reject H0. Fail to reject H0. A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at 2.1. The area under the curve to the right of 2.1 is shaded one color and labeled Reject Upper H 0. The area under the curve to the left of 2.1 is shaded another color and labeled Fail to reject Upper H 0. (c) Identify the standardized test statistic. Use technology. z=nothing (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 not sufficient evidence to reject the claim that mean bulb life is at least 744 hours. B. Fail to reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 744 hours. C. Reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 744 hours. D. Fail to reject H0. There is not sufficient evidence to reject the claim that mean bulb life is at least 744 hours. Click to select your answer(s).

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 744 hours. A random sample of 30 light bulbs has a mean life of 732 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≥744 (claim) Ha: μ<744 B. H0: μ≠744(claim) Ha: μ=744 C. H0: μ=732 Ha: μ≠732 (claim) D. H0: μ<732 (claim) Ha: μ≥732 E. H0: μ≤732 Ha: μ>732 (claim) F. H0: μ>744 Ha: μ≤744 (claim) (b) Identify the critical value(s). Use technology. z0=nothing (Use a comma to separate answers as needed. Round to two decimal places as needed.) Identify the rejection region(s). Choose the correct answer below. A. -404z Reject H0. Fail to reject H0. A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at negative 2.1. The area under the curve to the left of negative 2.1 is shaded one color and labeled Reject Upper H 0. The area under the curve to the right of negative 2.1 is shaded another color and labeled Fail to reject Upper H 0. B. -404z Reject H0. Reject H0. Fail to reject H0. A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segments extend from the horizontal axis to the curve at negative 2.1 and 2.1. The area under the curve to the left of negative 2.1 is shaded and the area under the curve to the right of 2.1 are both shaded one color and labeled Reject Upper H 0.The area under the curve between negative 2.1 and 2.1 is shaded another color and labeled Fail to reject Upper H 0. C. -404z Reject H0. Fail to reject H0. A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at 2.1. The area under the curve to the right of 2.1 is shaded one color and labeled Reject Upper H 0. The area under the curve to the left of 2.1 is shaded another color and labeled Fail to reject Upper H 0. (c) Identify the standardized test statistic. Use technology. z=nothing (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 not sufficient evidence to reject the claim that mean bulb life is at least 744 hours. B. Fail to reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 744 hours. C. Reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 744 hours. D. Fail to reject H0. There is not sufficient evidence to reject the claim that mean bulb life is at least 744 hours. Click to select your answer(s).

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

744

hours. A random sample of

light bulbs has a mean life of

732

hours. Assume the population is normally distributed and the population standard deviation is

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≥744

(claim)

Ha:

μ<744

H0:

μ≠744(claim)

Ha:

μ=744

H0:

μ=732

Ha:

μ≠732

(claim)

H0:

μ<732

(claim)

Ha:

μ≥732

H0:

μ≤732

Ha:

μ>732

(claim)

H0:

μ>744

Ha:

μ≤744

(claim)

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

z0=nothing

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

Identify the rejection region(s). Choose the correct answer below.

-404z

Reject H0.

Fail to reject H0.

A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at negative 2.1. The area under the curve to the left of negative 2.1 is shaded one color and labeled Reject Upper H 0. The area under the curve to the right of negative 2.1 is shaded another color and labeled Fail to reject Upper H 0.

-404z

Reject H0.

Fail to reject H0.

A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segments extend from the horizontal axis to the curve at negative 2.1 and 2.1. The area under the curve to the left of negative 2.1 is shaded and the area under the curve to the right of 2.1 are both shaded one color and labeled Reject Upper H 0.The area under the curve between negative 2.1 and 2.1 is shaded another color and labeled Fail to reject Upper H 0.

-404z

Reject H0.

Fail to reject H0.

A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at 2.1. The area under the curve to the right of 2.1 is shaded one color and labeled Reject Upper H 0. The area under the curve to the left of 2.1 is shaded another color and labeled Fail to reject Upper H 0.

z=nothing

(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

is not

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

744

hours.

Fail to reject

H0.

There

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

744

hours.

Reject

H0.

There

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

744

hours.

Fail to reject

H0.

There

is not

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

744

hours.

Click to select your answer(s).

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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