In a large midwestern university the class of entering fresh

In a large midwestern university (the class of entering freshmen being on the order of 6000 or more students), an SRS of 100 entering freshmen in 1999 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 1995. In 2001 an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. The proportion of all entering freshmen in 1999 and 2001, who graduated in the bottom third of their high school class, are p1 and p2, respectively. Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced, as a result of the tougher admission standards adopted in 2000, compared to the proportion in 1999?

To determine this, you test the hypotheses H0 : p1 = p2 , Ha : p1 > p2.

The p-value of your test is:

a. between .05 and .01

b. between .01 and .001

c. below .001

d. between .10 and .05

Solution

Null, There Is No Significance between them Ho: p1 = p2
Alternate, proportion of freshmen who graduated in 2001 has been reduced H1: p1 > p2
Test Statistic
Sample 1 : X1 =20, n1 =100, P1= X1/n1=0.2
Sample 2 : X2 =10, n2 =100, P2= X2/n2=0.1
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.15
Q^ Value For Proportion= 1-P^=0.85
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.2-0.1)/Sqrt((0.15*0.85(1/100+1/100))
Zo =1.98
| Zo | =1.98
Critical Value
The Value of |Z | at LOS 0.05% is 1.645
We got |Zo| =1.98 & | Z | =1.645
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail -Ha : ( P > 1.9803 ) = 0.02384
Hence Value of P0.05 > 0.02384,Here we Reject Ho

We have enough evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced

ANS: a. between .05 and .01