The admission office of a ASU finds that the rejection rate

The admission office of a ASU finds that the rejection rate of the applicant is 46.2%. The head wants to know how different the rejection rate is from other schools so the head randomly selects 10 other colleges and their rejection rates are as follows. Is ASU\'s rejection rate significantly different from others? Do we use a one-tail or two-tail test and why?
41%   44.2%   32.1%   36.4%   32.9%
46.4%   40.3%   51.7%   49.4%   29%

Solution

It\'s Two Tailed Test
Set Up Hypothesis
Null Hypothesis H0: U=46.2
Alternate Hypothesis H1: U!=46.2
Test Statistic
Population Mean(U)=46.2
Sample X(Mean)=40.34
Standard Deviation(S.D)=7.678
Number (n)=10
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =40.34-46.2/(7.678/Sqrt(9))
to =-2.414
| to | =2.414
Critical Value
The Value of |t | with n-1 = 9 d.f is 2.262
We got |to| =2.414 & | t | =2.262
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -2.4135 ) = 0.039
Hence Value of P0.05 > 0.039,Here we Reject Ho