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A research organization claims that the monthly wages of industrial workers in district X exceed those in district Y by more than Rs 150. Two different samples drawn independently from the two districts yielded the following results:

>District X: x1 bar = 648, 
s1^2 = 120, and 
n1 = 100 

>District Y: 
x2bar = 495, 
s2^2 = 140, and  n2 = 90

Verify at a 0.05 level of significance whether the sample results support the claim of the organization.

For this solutions I used the formula $$Z = \frac{\bar x_1- \bar x_2}{\sqrt{s_1^2/n_1+s_2^2/n_2}}$$ which gives me the answer $92.7$. Is this the correct Z-score how to verify it for a $0.05$ level of significance (new to this area)?

Can anyone tell me can I conclude since the result is 92.7 the results support the claim made by the research organization ?

user1403505
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  • Where did this formula come from? Have you carefully checked that you transcribed it correctly? – whuber Oct 02 '14 at 15:59
  • Hi Its a typo corrected now can you pls tell me the end result of calculating significance to this problem – user1403505 Oct 02 '14 at 16:09
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    There must still be some typos, because with the numbers you supply $Z=92.2$ rather than $95.6$. Moreover, with the changes you made to the question the values of $s_1$ and $s_2$ are not credible: monthly wages among so many workers would be unlikely to have such tiny variances. But no matter: you can find plenty of information about this test (look at http://stats.stackexchange.com/questions/30394 for instance) as well as on [how to interpret the test statistics](http://stats.stackexchange.com/search?q=t-test+p-value+critical). – whuber Oct 02 '14 at 17:31
  • Hi The values are sqr(s1) and sqr(s2) 120 and 140 which are correct and no typos in that – user1403505 Oct 02 '14 at 17:40

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