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 17 residents has a mean annual income of $ 40 comma 300 and a standard deviation of $ 8300. In County B, a random sample of 14 residents has a mean annual income of $ 37 comma 700 and a standard deviation of $ 5300. At alpha = 0.05. Assume the population variances are not equal. Assume the samples are random and independent, and the populations are normally distributed.
A) What are H0 and Ha?
B) Which hypothesis is the claim?
1) the alternative hypothesis, ha.
2) the null hypothesis, h0.
C) Find the critical value(s)a and identify the rejection region(s).
1) t<-t0,t>t0
2) t>t0
3) -t0 4) t<-t0
D) Find the standerized test statistic: t= ?
E) Decide whether to reject or fail to reject the null hypothesis.
F) 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?