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 $40,800 and a standard deviation of $8800. In County B, a random sample of 10 residents has a mean annual income of $40,000 and a standard deviation of $5800. At a = 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 H, and H. Which is the correct claim below? A. "The mean annual income in county A is greater than in county B." OB. "The mean annual income in county A is less than in county B." O C. "The mean annual incomes counties A and B are not equal." O D. "The mean annual incomes counties A and B are equal." What are Ho and H,? The null hypothesis, Ho, is H, s H2 . The alternative hypothesis, H, is u, >2 ·. Which hypothesis is the claim? * The alternative hypothesis, H O The null hypothesis, Ho b) Find the critical value(s) and identify the rejection region(s). Enter the critical value(s) below. Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)
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 $40,800 and a standard deviation of $8800. In County B, a random sample of 10 residents has a mean annual income of $40,000 and a standard deviation of $5800. At a = 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 H, and H. Which is the correct claim below? A. "The mean annual income in county A is greater than in county B." OB. "The mean annual income in county A is less than in county B." O C. "The mean annual incomes counties A and B are not equal." O D. "The mean annual incomes counties A and B are equal." What are Ho and H,? The null hypothesis, Ho, is H, s H2 . The alternative hypothesis, H, is u, >2 ·. Which hypothesis is the claim? * The alternative hypothesis, H O The null hypothesis, Ho b) Find the critical value(s) and identify the rejection region(s). Enter the critical value(s) below. Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)
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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Transcribed Image Text: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
$40,800 and a standard deviation of $8800. In County B, a random sample of 10 residents has a mean annual income of $40,000 and a standard deviation of $5800. At a = 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 H, and Ha.
Which is the correct claim below?
A. "The mean annual income in county A is greater than in county B."
B. "The mean annual income in county A is less than in county B."
C. "The mean annual incomes in counties A and B are not equal."
D. "The mean annual incomes in counties A and B are equal."
What are Ho and H,?
The null hypothesis, Ho, is µ1 sH2 - The alternative hypothesis, Ha, is µ1 > H2 -
Which hypothesis is the claim?
The alternative hypothesis, Ha
The null hypothesis, Ho
(b) Find the critical value(s) and identify the rejection region(s).
Enter the critical value(s) below.
(Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)
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