Question

California and New York lead the list of average teachers’ salaries. The California yearly average is $64,421 while teachers in New York make an average annual salary of $62,332. Random samples of 45 teachers from each state yielded the following.

	California	New York
Sample Mean	64,510	62,900
Population Standard Deviation	8,200	7,800

At a = 0.10, is there a difference in means of the salaries?

Note: I would like someone to please explain the process to find the answer step by step and also show me how to find this answer on Excel. I know how to find the answer for problems that contain data sets, but do not know how when there are not any datum.

Answer 1

null hypothesis: Ho:μ1-μ2			=	0
Alternate hypothesis: Ha:μ1-μ2			≠	0
for 0.1 level with two tail test , critical z=				1.645 (from excel function normsinv(0.95)

Decision rule : reject Ho if absolute value of test statistic |z|>1.645

	California		New York
x1            =	64510.00	x2            =	62900.00
n1           =	45	n2           =	45
σ1           =	8200.00	σ2           =	7800.00

std error σx1-x2=√(σ21/n1+σ22/n2)=sqrt(8200^2/45+7800^2/45) =

1687.0750

test stat z =(x1-x2-Δo)/σx1-x2    =(64510-62900)/1687.0750 =

0.95

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that population means differs