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 $42,100 and a standard deviation of $8500. In County B, a random sample of 10 residents has a mean annual income of $38,400 and a standard deviation of $5400. 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 Ho and H₂- 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." OD. "The mean annual incomes in counties A and B are equal." What are Ho and H₂? The null hypothesis. Ho. is The alternative hypothesis. Ha. is 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.) Select the correct rejection region(s) below. OA. to to D. t<-to. t>to (c) Find the standardized test statistic. t= ☐ (Type an integer or decimal rounded to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. the null hypothesis. (e) Interpret the decision in the context of the original claim. At the 0.5% significance level, enough evidence to support the personnel director's claim.
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 $42,100 and a standard deviation of $8500. In County B, a random sample of 10 residents has a mean annual income of $38,400 and a standard deviation of $5400. 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 Ho and H₂- 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." OD. "The mean annual incomes in counties A and B are equal." What are Ho and H₂? The null hypothesis. Ho. is The alternative hypothesis. Ha. is 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.) Select the correct rejection region(s) below. OA. to to D. t<-to. t>to (c) Find the standardized test statistic. t= ☐ (Type an integer or decimal rounded to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. the null hypothesis. (e) Interpret the decision in the context of the original claim. At the 0.5% significance level, enough evidence to support the personnel director's claim.
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 $42,100 and a standard deviation of $8500. In County B, a random sample of 10
residents has a mean annual income of $38,400 and a standard deviation of $5400. 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 Ho and H₂-
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."
OD. "The mean annual incomes in counties A and B are equal."
What are Ho and H₂?
The null hypothesis. Ho. is
The alternative hypothesis. Ha. is
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.)
Transcribed Image Text:Select the correct rejection region(s) below.
OA. to <t<to
○ B. t<-to
○ C. t> to
D. t<-to. t>to
(c) Find the standardized test statistic.
t= ☐ (Type an integer or decimal rounded to three decimal places as needed.)
(d) Decide whether to reject or fail to reject the null hypothesis.
the null hypothesis.
(e) Interpret the decision in the context of the original claim.
At the 0.5% significance level,
enough evidence to support the personnel director's claim.
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