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Math Help - Quick question on confidence intervals

  1. #1
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    Quick question on confidence intervals

    Ten engineering schools in the US were surveyed. The sample contained 250 electrical engineers, 80 being women, and 175 chemical engineers, 40 being women. Compute a 90% confidence interval for the difference between the porportion of women in these two fields of engineering. Is there a significant difference between the two proportions?

    I calculated the confidence interval and got:

    0.091+/-0.043

    I'm a bit stuck on answering the bolded part though.

    I would say that there is a significant difference between the two proportions because the 90% confidence interval doesn't include 0.

    Is this correct? Thanks
    Last edited by downthesun01; October 9th 2010 at 04:18 PM.
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  2. #2
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    Quote Originally Posted by downthesun01 View Post
    Ten engineering schools in the US were surveyed. The sample contained 250 electrical engineers, 80 being women, and 175 chemical engineers, 40 being women. Compute a 90% confidence interval for the difference between the porportion of women in these two fields of engineering. Is there a significant difference between the two proportions?

    I calculated the confidence interval and got:

    0.091+/-0.043

    I'm a bit stuck on answering the bolded part though.

    I would say that there is a significant difference between the two proportions because the 90% confidence interval doesn't include 0.

    Is this correct? Thanks
    What did you get for the SE of the difference of the two proportions?

    The 90% confidence interval is the observed difference +/- 1.645*SE

    CB
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    SE=\frac{0.043}{1.645}\approx 0.0261
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    Quote Originally Posted by downthesun01 View Post
    SE=\frac{0.043}{1.645}\approx 0.0261
    No, I know what its value is and how to calculate it, what I want to know is how you calculated it, or rather how you calculated the length of the confidence interval (it's a bit like a hint that I think that it is wrong).

    CB
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    \sqrt{\frac{(0.32)(0.68)}{250}+{\frac{(0.229)(0.77  1)}{175}}}=\sqrt{0.001879308571}\approx 0.043
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    Quote Originally Posted by downthesun01 View Post
    \sqrt{\frac{(0.32)(0.68)}{250}+{\frac{(0.229)(0.77  1)}{175}}}=\sqrt{0.001879308571}\approx 0.043
    The 90% confidence interval is the observed difference +/- 1.645*SE
    So the confidence interval is: .... ?

    CB
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    pr(0.091-0.043<P_{a}-P_{b}<0.091+0.043)=0.9

    pr(0.48<P_{a}-P_{b}<0.139)=0.9

    If there's something that you're trying to help me see, I'm totally not getting it sorry.
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  8. #8
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    Quote Originally Posted by downthesun01 View Post
    pr(0.091-0.043<P_{a}-P_{b}<0.091+0.043)=0.9

    pr(0.48<P_{a}-P_{b}<0.139)=0.9

    If there's something that you're trying to help me see, I'm totally not getting it sorry.
    Read what has been posted in this thread, we know what the observed difference Ob, is (0.091), we know what the standard error SE of this difference is (0.0433..) and we know the 90% confidence interval is [Ob-1.645.SE, Ob+1.645.SE], so ....

    What I want you to see is that the confidence interval is:

    [0.091-1.645\times 0.0433, 0.091+1.645\times 0.0433]\approx [0.091-0.071,0.091+0.071]=[0.020,0.162]

    In other words I want you to calculate the confidence interval correctly.

    CB
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    Oh. You're right. That's what I have written down on paper. Typing all this through my phone is a bit tedious. My mistake.

    However, it still leaves me wondering the difference between the two proportions is significant. I'll just say yes. Thanks
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  10. #10
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    Quote Originally Posted by downthesun01 View Post
    Oh. You're right. That's what I have written down on paper. Typing all this through my phone is a bit tedious. My mistake.

    However, it still leaves me wondering the difference between the two proportions is significant. I'll just say yes. Thanks
    Since zero is not in the confidence interval, the difference is significant at this level.

    CB
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