Answered: Test a claim that the mean amount of…

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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Part 1

(a) Identify the claim and state

and

Ha.

H0:	▼ sigma squaredσ2 pp muμ sigmaσ ▼ greater than or equals≥ greater than> not equals≠ equals= less than or equals≤ less than< enter your response here
Ha:	▼ sigma squaredσ2 sigmaσ muμ pp ▼ greater than> less than< greater than or equals≥ less than or equals≤ not equals≠ equals= enter your response here

(Type integers or decimals. Do not round.)

The claim is the

▼

alternative

null

hypothesis.

Part 2

(b) Find the critical value(s) and identify the rejection region(s).

The critical value(s) is/are

t0=enter your response here.

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

Part 3

Choose the graph which shows the rejection region.

0 -44t

−t0

t<−t0, t>t0

A graph labeled t less than negative t 0, t greater than t 0 has a horizontal t-axis labeled from negative 4 to 4 in increments of 4. A symmetric bell shaped t-distribution curve is above the t-axis and centered on 0. Two vertical line segments extend from the curve to the t-axis at the points labeled negative t 0 and t 0, where t 0 is to the right of 0. The areas under the curve to the left of negative t 0 and to the right of t 0 are shaded.

-4 0 4 t

t<t0

A graph labeled t less than t 0 has a horizontal t-axis labeled from negative 4 to 4 in increments of 4. A symmetric bell shaped t-distribution curve is above the t-axis and centered on 0. A vertical line segment extends from the curve to the t-axis at a point labeled t 0, where t 0 is to the left of 0. The area under the curve to the left of t 0 is shaded.

0 -44t

−t0

−t0<t<t0

A graph labeled negative t 0 less than t less than t 0 has a horizontal t-axis labeled from negative 4 to 4 in increments of 4. A symmetric bell shaped t-distribution curve is above the t-axis and centered on 0. Two vertical line segments extend from the curve to the t-axis at the points labeled negative t 0 and t 0, where t 0 is to the right of 0. The area under the curve between negative t 0 and t 0 is shaded.

-4 0 4 t

t>t0

A graph labeled t greater than t 0 has a horizontal t-axis labeled from negative 4 to 4 in increments of 4. A symmetric bell shaped t-distribution curve is above the t-axis and centered on 0. A vertical line segment extends from the curve to the t-axis at a point labeled t 0, where t 0 is to the right of 0. The area under the curve to the right of t 0 is shaded.

Part 4

The standardized test statistic is

t=enter your response here.

(Round to two decimal places as needed.)

Part 5

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

▼

Reject

Fail to reject

because the standardized test statistic

▼

is not

in the rejection region.

Part 6

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

There

▼

is not

enough evidence at the

enter your response here%

level of significance to

▼

rejectreject

supportsupport

the claim that the mean amount of lead in the air in U.S. cities is

▼

less than

equal

greater than

greater than or equal

not equal

less than or equal

enter your response here

microgram per cubic meter.

(Type integers or decimals. Do not round.)

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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