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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 18 residents has a mean annual income of $40,400 and a standard deviation of $9000. In County B, a random sample of 8 residents has a mean annual income of $38,900 and a standard deviation of $5200. At a = 0.10, 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 Ho and Ha Which is the correct claim below? OA. "The mean annual incomes in Counties A and B are equal." B. "The mean annual income in County A is less than in County B." OC. "The mean annual incomes in Counties A and B are not equal." O D. "The mean annual income in County A is greater than in County B." What are Ho and H₂? The null hypothesis, Ho, is Which hypothesis is the claim? O The alternative hypothesis, Ha O The null hypothesis, Ho The alternative hypothesis, Ha, is (b) Find the critical value(s) and identify the rejection region(s). Enter the critical value(s) below. n

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 18 residents has a mean annual income of $40,400 and a standard deviation of $9000. In County B, a random sample of 8 residents has a mean annual income of $38,900 and a standard deviation of $5200. At a = 0.10, 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 Ho and Ha Which is the correct claim below? OA. "The mean annual incomes in Counties A and B are equal." B. "The mean annual income in County A is less than in County B." OC. "The mean annual incomes in Counties A and B are not equal." O D. "The mean annual income in County A is greater than in County B." What are Ho and H₂? The null hypothesis, Ho, is Which hypothesis is the claim? O The alternative hypothesis, Ha O The null hypothesis, Ho The alternative hypothesis, Ha, is (b) Find the critical value(s) and identify the rejection region(s). Enter the critical value(s) below. n

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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 18 residents has a mean annual income of $40,400 and a standard deviation of $9000. In County B, a random sample of 8 residents has a mean annual income of $38,900 and a standard deviation of $5200. At a = 0.10, 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. Enter the critical value(s) below. (Type an integer or decimal rounded to three decimal places as needed. Use comma to separate answers as needed.) Select the correct rejection region(s) below. O A. t>to OB. t-to. t>to O C. -to <t<to O D. 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.
Transcribed Image Text: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 18 residents has a mean annual income of $40,400 and a standard deviation of $9000. In County B, a random sample of 8 residents has a mean annual income of $38,900 and a standard deviation of $5200. At a = 0.10, 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. Enter the critical value(s) below. (Type an integer or decimal rounded to three decimal places as needed. Use comma to separate answers as needed.) Select the correct rejection region(s) below. O A. t>to OB. t-to. t>to O C. -to <t<to O D. 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.
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 18 residents has a mean annual income of $40,400 and a standard deviation of $9000. In County B, a random sample of 8 residents has a mean annual income of $38,900 and a standard deviation of $5200. At x = 0.10, 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 Ho and Ha Which is the correct claim below? OA. "The mean annual incomes in Counties A and B are equal." B. "The mean annual income in County A is less than in County B." OC. "The mean annual incomes in Counties A and B are not equal." O D. "The mean annual income in County A is greater than in County B." What are Ho and Ha? The null hypothesis, Ho, is Which hypothesis is the claim? O The alternative hypothesis, Ha O The null hypothesis, Ho The alternative hypothesis, Ha, is (b) Find the critical value(s) and identify the rejection region(s). Enter the critical value(s) below. n C
Transcribed Image Text: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 18 residents has a mean annual income of $40,400 and a standard deviation of $9000. In County B, a random sample of 8 residents has a mean annual income of $38,900 and a standard deviation of $5200. At x = 0.10, 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 Ho and Ha Which is the correct claim below? OA. "The mean annual incomes in Counties A and B are equal." B. "The mean annual income in County A is less than in County B." OC. "The mean annual incomes in Counties A and B are not equal." O D. "The mean annual income in County A is greater than in County B." What are Ho and Ha? The null hypothesis, Ho, is Which hypothesis is the claim? O The alternative hypothesis, Ha O The null hypothesis, Ho The alternative hypothesis, Ha, is (b) Find the critical value(s) and identify the rejection region(s). Enter the critical value(s) below. n C
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