Test a claim that the mean amount of lead in the air in U.S. cities is less than 0.038 microgram per cubic meter. It was found that the mean amount of lead in the air for the random sample of 56 U.S. cities is 0.038 microgram per cubic meter and the standard deviation is 0.068 microgram per cubic meter. At alphaαequals=0.01, can the claim be supported? Complete parts (a) through (e) below. Assume the population is normally distributed. (a) Identify the claim and state Upper H 0H0 and Upper H Subscript aHa. Upper H 0 : nbspH0: ▼ sigma squaredσ2 pp sigmaσ muμ ▼ less than or equals≤ greater than> not equals≠ less than< greater than or equals≥ equals= nothing Upper H Subscript a Baseline : nbspHa: ▼ muμ pp sigmaσ sigma squaredσ2 ▼ less than or equals≤ greater than or equals≥ equals= not equals≠ less than< greater than> nothing (Type integers or decimals. Do not round.) The claim is the ▼ alternative null hypothesis. (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is/are t 0t0equals=nothing. (Use a comma to separate answers as needed. Round to two decimal places as needed.) Choose the graph which shows the rejection region. A. 0 -44t negative t 0−t0 t 0t0 negative t 0 less than t less than t 0−t0t0 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. C. -4 0 4 t t 0t0 t less than t 0tt0 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. (c) Find the standardized test statistic, t. The standardized test statistic is tequals=nothing. (Use a comma to separate answers as needed. Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. ▼ Fail to reject Reject Upper H 0H0 because the standardized test statistic ▼ is is not in the rejection region. (e) Interpret the decision in the context of the original claim. There ▼ is not is enough evidence at the nothing% level of significance to ▼ rejectreject supportsupport the claim that the mean amount of lead in the air in U.S. cities is ▼ equal greater than or equal less than or equal not equal greater than less than nothing microgram per cubic meter. (Type integers or decimals. Do not round.)

Test a claim that the mean amount of lead in the air in U.S. cities is less than 0.038 microgram per cubic meter. It was found that the mean amount of lead in the air for the random sample of 56 U.S. cities is 0.038 microgram per cubic meter and the standard deviation is 0.068 microgram per cubic meter. At alphaαequals=0.01, can the claim be supported? Complete parts (a) through (e) below. Assume the population is normally distributed. (a) Identify the claim and state Upper H 0H0 and Upper H Subscript aHa. Upper H 0 : nbspH0: ▼ sigma squaredσ2 pp sigmaσ muμ ▼ less than or equals≤ greater than> not equals≠ less than< greater than or equals≥ equals= nothing Upper H Subscript a Baseline : nbspHa: ▼ muμ pp sigmaσ sigma squaredσ2 ▼ less than or equals≤ greater than or equals≥ equals= not equals≠ less than< greater than> nothing (Type integers or decimals. Do not round.) The claim is the ▼ alternative null hypothesis. (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is/are t 0t0equals=nothing. (Use a comma to separate answers as needed. Round to two decimal places as needed.) Choose the graph which shows the rejection region. A. 0 -44t negative t 0−t0 t 0t0 negative t 0 less than t less than t 0−t0t0 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. C. -4 0 4 t t 0t0 t less than t 0tt0 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. (c) Find the standardized test statistic, t. The standardized test statistic is tequals=nothing. (Use a comma to separate answers as needed. Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. ▼ Fail to reject Reject Upper H 0H0 because the standardized test statistic ▼ is is not in the rejection region. (e) Interpret the decision in the context of the original claim. There ▼ is not is enough evidence at the nothing% level of significance to ▼ rejectreject supportsupport the claim that the mean amount of lead in the air in U.S. cities is ▼ equal greater than or equal less than or equal not equal greater than less than nothing microgram per cubic meter. (Type integers or decimals. Do not round.)

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

Test a claim that the mean amount of lead in the air in U.S. cities is less than

0.038

microgram per cubic meter. It was found that the mean amount of lead in the air for the random sample of

U.S. cities is

0.038

microgram per cubic meter and the standard deviation is

0.068

microgram per cubic meter. At

alphaαequals=0.01,

can the claim be supported? Complete parts (a) through (e) below. Assume the population is normally distributed.

(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

Upper H 0 : nbspH0:	▼ sigma squaredσ2 pp sigmaσ muμ ▼ less than or equals≤ greater than> not equals≠ less than< greater than or equals≥ equals= nothing
Upper H Subscript a Baseline : nbspHa:	▼ muμ pp sigmaσ sigma squaredσ2 ▼ less than or equals≤ greater than or equals≥ equals= not equals≠ less than< greater than> nothing

(Type integers or decimals. Do not round.)

The claim is the

▼

alternative

null

hypothesis.

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

The critical value(s) is/are

t 0t0equals=nothing.

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

Choose the graph which shows the rejection region.

0 -44t

negative t 0−t0

t 0t0

negative t 0 less than t less than t 0−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 0t0

t greater than t 0t>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.

-4 0 4 t

t 0t0

t less than t 0t<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

negative t 0−t0

t 0t0

t less than minus t 0 comma t greater than t 0t<−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.

The standardized test statistic is

tequals=nothing.

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

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

▼

Fail to reject

Reject

Upper H 0H0

because the standardized test statistic

▼

is not

in the rejection region.

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

There

▼

is not

enough evidence at the

nothing%

level of significance to

▼

rejectreject

supportsupport

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

▼

equal

greater than or equal

less than or equal

not equal

greater than

less than

nothing

microgram per cubic meter.

(Type integers or decimals. Do not round.)

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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