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 6 residents has a mean annualincome of $41,400 and a standard deviation of $8400. In County B, a random sample of 8 residents has a mean annual income of $39,800 and a standard deviation of $5200. At a = 0.10, answer parts (a) through (e). Assume thepopulation variances are not equal. If convenient, use technology to solve the problem.(a) Identify the claim and state Ho 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 H, and Ha?The null hypothesis, Ho, isThe alternative hypothesis, Ha, isWhich hypothesis is the claim?The null hypothesis, HoThe alternative hypothesis, Ha(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.A. -to toO C. t< -toO D. t>to (c) Find the standardized test statistic.t3=(Type an integer or decimal rounded to three decimal places as needed.)(d) Decide whether to reject or fail to reject the null hypothesis.V the null hypothesis.(e) Interpret the decision in the context of the original claim.At the 10% significance level,enough evidence to support the personnel director's claim.

Given information: It is claimed that the mean annual income is greater in county A than in county…

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 6 residents has a mean annual income of $41,400 and a standard deviation of $8400. In County B, a random sample of 8 residents has a mean annual income of $39,800 and a standard deviation of $5200. At a = 0.10, answer parts (a) through (e). Assume the population variances are not equal. convenient, use technology to solve the problem. (a) Identify the claim and state Ho and H. Which is the correct claim below? O A. "The mean annual income in county A is less than county B." O B. "The mean annual incomes in counties A and B are not equal." OC. "The mean annual incomes in counties A and B are equal." O D. "The mean annual income in county A is greater than county B." What are Ho and H,? The null hypothesis, Ho, is The alternative hypothesis, Ha. is Which hypothesis is the claim? O The null hypothesis, Ho O The alternative hypothesis, Ha (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 -toto OC. t< -to O D. t>h

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA