Answered: (e) Interpret the decision in the…

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 company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is

milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of

52.4

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

7.4

milligrams. At

α=0.10,

can you reject the company's claim? Complete parts (a) through (e).

(a) Identify

and

Ha.

Choose the correct answer below.

H0:

μ=50

Ha:

μ≠50

Your answer is correct.

H0:

μ≠50

Ha:

μ=50

H0:

μ≥52.4

Ha:

μ<52.4

H0:

μ≥50

Ha:

μ<50

H0:

μ≠52.4

Ha:

μ=52.4

H0:

μ=52.4

Ha:

μ≠52.4

(b) Find the critical value(s). Select the correct choice below and fill in the answer box within your choice.

(Round to two decimal places as needed.)

The critical values are

±1.651.65.

Your answer is correct.

The critical value is

enter your response here.

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

-404z

Reject H0.

Fail to reject H0.

A normal curve is over a horizontal axis labeled z from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segment extends to the right of 0 from the horizontal axis to the curve. The area under the curve to the right of the line segment is shaded and labeled Reject H@Sub{0}. The area under the curve to the left of the line segment is labeled Fail to reject H@Sub{0}.

-404z

Reject H0.

Fail to reject H0.

A normal curve is over a horizontal axis labeled z from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segment extends to the left of 0 from the horizontal axis to the curve. The area under the curve to the left of the line segment is shaded and labeled Reject H@Sub{0}. The area under the curve to the right of the line segment is labeled Fail to reject H@Sub{0}.

-404z

Reject H0.

Fail to reject H0.

A normal curve is over a horizontal axis labeled z from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segments extend to the left of and to the right 0 from the horizontal axis to the curve. The area under the curve the left of the left line segment and to the right of the right lines segment is shaded and labeled Reject H@Sub{0}. The area between the vertical line segments is labeled Fail to reject H@Sub{0}.

Your answer is correct.

z=1.781.78

(Round to two decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis.

Since z

is not

in the rejection region,

reject

the null hypothesis.

Since z

is not

in the rejection region,

fail to reject

the null hypothesis.

Since z

in the rejection region,

fail to reject

the null hypothesis.

Since z

in the rejection region,

reject

the null hypothesis.

Your answer is correct.

(e) Interpret the decision in the context of the original claim.

At the

10%

significance level, there

▼

is not

enough evidence to

▼

reject

support

the company's claim that the mean caffeine content per 12-ounce bottle of cola

▼

is equal to

is greater than

is different from

is less than

enter your response here

milligrams.

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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