A personnel director in a particular state claims that the mean annual income is the same in one of the state's counties (County A) as it is in another county (County B). In County A, a random sample of 17 residents has a mean annual income of $42,100 and a standard deviation of $8300.In County B, a random sample of 14 residents has a mean annual income of $37,900 and a standard deviation of $5700. At α=0.05, answer parts (a) through (e). Assume the population variances are not equal. Assume the samples are random and independent, and the populations are normally distributed. (a) Identify the claim and state Upper H 0H0 and Upper H Subscript aHa. Which is the correct claim below? A. "The mean annual incomes in Counties A and B are not equal." B. "The mean annual incomes in Counties A and B are equal." This is the correct answer. C. "The mean annual income in County A is greater than in County B." D. "The mean annual income in County A is less than in County B." What are Upper H 0H0and Upper H Subscript aHa? The null hypothesis, Upper H 0H0, is mu 1 equals mu 2 .μ1=μ2. The alternative hypothesis, Upper H Subscript aHa, is mu 1 not equals mu 2 .μ1≠μ2. Which hypothesis is the claim? The alternative hypothesis, Upper H Subscript aHa The null hypothesis, Upper H 0H0 Your answer is correct. (b) Find the critical value(s) and identify the rejection region(s). Enter the critical value(s) below.

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Description: A personnel director in a particular state claims that the mean annual income is the same in one of the state's counties (County A) as it is in another county (County B). In County A, a random sample of 17 residents has a mean annual income of $4

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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A personnel director in a particular state claims that the mean annual income is the same in one of the state's counties (County A) as it is in another county (County B). In County A, a random sample of 17 residents has a mean annual income of $42,100 and a standard deviation of $8300.
In County B, a random sample of 14 residents has a mean annual income of

$37,900 and a standard deviation of $5700. At α=0.05,

answer parts (a) through (e). Assume the population variances are not equal. Assume the samples are random and independent, and the populations are normally distributed.

(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

Which is the correct claim below?

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

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

This is the correct answer.

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

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

What are Upper H 0H0
and Upper H Subscript aHa?

The null hypothesis,

Upper H 0H0,

mu 1 equals mu 2 .μ1=μ2.

The alternative hypothesis,

Upper H Subscript aHa,

mu 1 not equals mu 2 .μ1≠μ2.

Which hypothesis is the claim?

The alternative hypothesis, Upper H Subscript aHa

The null hypothesis, Upper H 0H0

Your answer is correct.

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

Enter the critical value(s) below.

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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