
Statistics
Hi everyone, I am having trouble with this question. Can anyone help me answer it. Thanks
[FONT='Tahoma','sansserif']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]

$\displaystyle H_{0}: \mu=0.5 $
$\displaystyle H_{1}: \mu<0.5\\$
$\displaystyle X \sim B(100, 0.5) \ np=50, \ npq=25\\$
$\displaystyle \Rightarrow X \approx N(50, 25)\\$
$\displaystyle \overline{X} \approx N(50, \frac{25}{100})\\$
$\displaystyle P(X \leq48) \Rightarrow P(\overline{X} \leq48.5)\\$
$\displaystyle = \Phi\frac{48.550}{\sqrt{\frac{25}{100}}}$
$\displaystyle =0.00135 < 0.05$
$\displaystyle \Rightarrow $Reject $\displaystyle H_{0}$