A personnel director in a particular state claims that the mean annual income is greater in one of the state's counties (county A) than it is in another county (county B). In County A, a random sample of 12 residents has a mean annual income of $40,300 and a standard deviation of $ 8900 In County B, a random sample of 10 residents has a mean annual income of $39,900 and a standard deviation of $5100. At alphaαequals=0.005, answer parts (a) through (e). Assume the population variances are not equal. If convenient, use technology to solve the problem. (a) Identify the claim and state H0 and Ha. Which is the correct claim below? A. "The mean annual income in county A is less than in county B." B. "The mean annual incomes in counties A and B are not equal." C. "The mean annual incomes in counties A and B are equal." D. "The mean annual income in county A is greater than in county B." What are H0 and Ha? The null hypothesis, H0, is ▼ μ1=μ2 μ1≤μ2 μ1≥μ2 . The alternative hypothesis, Ha, is ▼ μ1≠μ2 μ1>μ2 μ1<μ2 . Which hypothesis is the claim? The alternative hypothesis, Ha The null hypothesis, H0 (b) Find the critical value(s) and identify the rejection region(s). Enter the critical value(s) below. nothing (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) Select the correct rejection region(s) below. A. t>t0 B. t<−t0, t>t0 C. t<−t0 D. −t0

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 personnel director in a particular state claims that the mean annual income is greater in one of the state's counties (county A) than it is in another county (county B). In County A, a random sample of

residents has a mean annual income of

$40,300

and a standard deviation of

$ 8900

In County B, a random sample of

residents has a mean annual income of

$39,900

and a standard deviation of

$5100.

alphaαequals=0.005,

answer parts (a) through (e). Assume the population variances are not equal. If convenient, use technology to solve the problem.

(a) Identify the claim and state

and

Ha.

Which is the correct claim below?

"The mean annual income in county A is less than in county B."

"The mean annual incomes in counties A and B are not equal."

"The mean annual incomes in counties A and B are equal."

"The mean annual income in county A is greater than in county B."

What are

and

Ha?

The null hypothesis,

H0,

▼

μ1=μ2

μ1≤μ2

μ1≥μ2

The alternative hypothesis,

Ha,

▼

μ1≠μ2

μ1>μ2

μ1<μ2

Which hypothesis is the claim?

The alternative hypothesis, Ha

The null hypothesis, H0

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

Enter the critical value(s) below.

nothing

(Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)

Select the correct rejection region(s) below.

t>t0

t<−t0, t>t0

t<−t0

−t0<t<t0

tequals=nothing

(Type an integer or decimal rounded to three decimal places as needed.)

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

▼

Fail to reject

Reject

the null hypothesis.

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

At the

0.5 %

significance level,

▼

there is not

there is

enough evidence to support the personnel director's claim.

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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