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Math Help - Statistics

  1. #1
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    Jun 2008
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    Statistics

    Hi everyone, I am having trouble with this question. Can anyone help me answer it. Thanks

    [FONT='Tahoma','sans-serif']Research at the University of Toledo indicates that 50 percent of the students change their major area of study after their first year in a program. A random sample of 100 students in the College of Business revealed that 48 had changed their major area of study after their first year of the program. Has there been a significant decrease in the proportion of students who change their major after the first year in this program? Test at the .05 level of significance.[/FONT]
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  2. #2
    Junior Member
    Joined
    Mar 2008
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    H_{0}: \mu=0.5

    H_{1}: \mu<0.5\\

    X \sim B(100, 0.5) \ np=50, \ npq=25\\

    \Rightarrow X \approx N(50, 25)\\

    \overline{X} \approx N(50, \frac{25}{100})\\

    P(X \leq48) \Rightarrow P(\overline{X} \leq48.5)\\

    = \Phi\frac{48.5-50}{\sqrt{\frac{25}{100}}}

    =0.00135 < 0.05
    \Rightarrow Reject H_{0}
    Last edited by Nyoxis; June 10th 2008 at 04:54 PM.
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