Data on graduation rates was collected from a local high school. The following i
ID: 3381468 • Letter: D
Question
Data on graduation rates was collected from a local high school. The following information was gathered:
Gender Number of Students Number who graduated
Female 460 391
Male 650 507
a. Find the interval estimation for the difference between the proportions of females versus males who graduate. Use ?=.05.
b. Find the test statistic for testing for the difference between the two proportions.
Explanation / Answer
Null Hypothesis, There Is No Significance between them Ho: p1 = p2
Alternate Hypothesis, There Is Significance between them H1: p1 != p2
Test Statistic
Sample 1 : X1 =391, n1 =460, P1= X1/n1=0.85
Sample 2 : X2 =507, n2 =650, P2= X2/n2=0.78
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.809
Q^ Value For Proportion= 1-P^=0.191
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.85-0.78)/Sqrt((0.809*0.191(1/460+1/650))
Zo =2.923
| Zo | =2.923
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =2.923 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != 2.9227 ) = 0.0035
Hence Value of P0.05 > 0.0035,Here we Reject Ho
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