# Statistics

• Jun 10th 2008, 08:45 AM
hughes1m
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]
• Jun 10th 2008, 03:50 PM
Nyoxis
$H_{0}: \mu=0.5$

$H_{1}: \mu<0.5\\$

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

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

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

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

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

$=0.00135 < 0.05$
$\Rightarrow$Reject $H_{0}$