*** types of phone *** system are *** tested *** determine if there is *** dierence *** the proportions of
system failures (crashes). *** out of a *** sample of 150 *** *** *** *** system *** within
the *** eight *** *** *** *** *** of *** random *** *** 150 phones *** OS2 had system
failures *** *** rst eight *** of *** *** is *** to *** more *** (have *** crashes) *** *** appropriate hypothesis.
Solution
Given that *** *** 150
,X
1= *** = 150
andX
2= 9
.
The sample proportions are *** = X
1 n
1 *** *** *** .
^
p
2 *** X
2 *** *** *** 0
:06 .
The *** estimate *** sample proportion is *** = X
1+
X
2 *** =
15+9 150+150
= *** 1 *** *** hypothesis *** *** hypothesis *** *** is
H *** =
p
2 against
H
1:
p
1 *** *** )
Step 2 Dene test statistic
The test statistic *** testing above *** *** *** *** ( ***
^
p
2)
***
p
2) q
^
p *** ^
p ) n
1 +^
p *** ^
p *** n
2 *** *** statistic Zfollows *** *** distribution *** *** 3 Specify *** *** *** *** *** signicance level *** *** *** *** *** 4 Determine the critical value
As the *** hypothesis isright-tailed, *** *** value ofZ is *** Normal Statistical *** rejection region *** critical *** is Z *** *** 5 Computation
The *** *** under *** *** *** is
Zobs =( ***
^
p
2)
(p
1
p
2) q
^
p *** ^
p *** *** *** *** ^
p *** n
2
= *** *** 0 q
0
:08 *** *** 150
+0
:08 (1 *** *** 1 *** *** Decision
Traditional *** *** *** (i.e. critical *** isZ > 1.64. The *** *** *** *** *** fallsoutsidethe
critical *** *** *** *** rejectthe *** *** -value *** test isright-tailedtest, so the p-value is *** *** to *** the test statistic (Z
obs= 1:277) is *** 0:1008 .
The *** *** isgreater thanthe *** level of= *** *** to *** *** conclude that *** *** no sucient evidence to reject *** null *** so *** *** do not *** *** has *** *** failures than OS1.
2