Question

Past records suggest that the mean annual income, Hy, of teachers in state of California is less than or equal to the mean annual income, My, of teachers in Oregon. In a current study, a random sample of 10 teachers from California and an independent random sample of 10 teachers from Oregon have been asked to report their mean annual income. The data obtained are as follows: Annual income in dollars California 43096, 44370, 53093, 52462, 41185,49592,41491, 45798,43632, 48322 Oregon 46049,38659,49394,42895,45701, 48633, 46794, 44133,49644,52528 The population standard deviation for mean annual income of teachers in California and in Oregon are estimated as 6100 and 6200, respectively. It is also known that both populations are approximately normally distributed. At the 0.1 level of significance, is there sufficient evidence to reject the claim that the mean annual income of teachers in state of California is less than or equal to the mean annual income of teachers in Oregon? Perform a one-tailed test. Then in in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

Answer 1

C629 fx =AVERAGE(C615:0624) A B с D 61 612 613 California 43096 Oregon 46049 44370 53093 38659 49394 42895 45701 52462 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 41185 49592 41491 45798 43632 48322 48633 46794 44133 49644 52528 Mean 1= 46304.1 Mean 2= 46443

Given

$\sigma _{1}$=6100

$\sigma _{2}$ =6200

n1= 10

n2= 10

$\alpha$ =0.10

also we have

$\bar{x_{1}}$ = 46304.1

$\bar{x_{2}}$ = 46443

H0: $\mu _{1} =\mu _{2}$

H1:$\mu _{1} < \mu _{2}$

Test statistics Z since population sd are given

$Z=\frac{\bar{x_{1}}-\bar{x_{2}}}{\sqrt{\sigma _{1}^{2}/n1+\sigma _{2}^{2}/n2}}$

$Z= \frac{-138.9}{2750.454508} = -0.0505$

Z = -0.051

p-value = 0.4798

Conclusion : p-value (0.4798) > 0.10

Fail to Reject Ho

Can we reject the claim that the mean annual income of teachers from California is less than or equal to the mean annual income of teachers from Oregon? Yes

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