Question

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 country A, a random sample of 13 residents has a mean annual income of 42,200 and a standard deviation of 9000. in county b, a random sample of 11 residents has a mean annual income of 39800 and a standard deviation of 5200. at a=.025, answer parts a-e. assume the population variances are not equal.
a) what are H0 and Ha?

The null hypothesis, h0, is u1or u1=u2 or u1/>u2. The alternateive hypothesis, Ha, is u1>u2 or u1/=u2 or u1
Which hypothesis is the claim?

1) the alternative hypothesis, ha

2) the null hypothesis, h0

b) find the critical value(s)a and identify the rejection region(s).

enter the correct critical value(s):

select the correct rejection region(s) below:

1)t<-t0,t>t0

2)t>t0

3)-t0
4)t<-t0

c)find the standerized test statistic:

t= ?

d) decide whether to reject or fail to reject the null hypothesis.

e)interpert the decision in the context of the original claim:

at 2.5% significance level, there is or there is not enough evidence to support the personnel director's claim?

Answer 1

Answer:

Kindly see explaination.

Step-by-step explanation:

a) )H0: u1= u2

Ha:u1>u2

the claim is

1) the alternative hypothesis, ha

See formular at attachment please.

b) using above formula( see formula in attachment)

degree of freedom=v=19

so critical value=2.093

rejection region:2)t>t0

c)test statistics=(42200-39800)/sqrt(9000^2/13+5200^2/11)=0.8142

d)so we fail to reject H0

e)at 2.5% significance level, there is not enough evidence to support the personnel director's claim.