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...


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 13 residents has a mean annual income of $40,100 and a standard deviation of $8100. In County? B, a random sample of 11 residents has a mean annual income of $38,500 and a standard deviation of $5700. Ar ?= 0.025,


answer parts? (a) through? (e). Assume the population variances are not equal. If convenient, use technology to solve the problem.


a. Which is the correct claim​ below?




A.


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




B.


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




C.


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




D.


​"The mean annual incomes in counties A and B are not​ equal"


B.
What are H0 and Ha​?


The Null Hypoythesis, H0, is _____. The Alternative hypothese, Ha is ________



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

Enter the critical​ value(s) below.


Select the correct rejection​ region(s) below.



C.


Find the standardized test statistic.


t=


D.  Decide whether to reject or fail to reject the null hypothesis.


E. Interpret the decision in the context of the original claim.

At the ____ significance​ level, there ______ enough evidence to support the personnel​ director's claim.










Jun 08, 2022
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