You wish to test the following claim (H1) at a significance
level of α=0.10.
Ho:p1=p2
H1:p1<p2
You obtain a sample from the first population with 423 successes
and 41 failures. You obtain a sample from the second population
with 294 successes and 25 failures.
What is the critical value for this test? (Report answer accurate
to three decimal places.)
critical value =
What is the test statistic for this sample? (Report answer accurate
to three decimal places.)
test statistic =
The test statistic is...
This test statistic leads to a decision to...
As such, the final conclusion is that...
Null and
Ho:p1=p2
H1:p1<p2
Pooled proportion=p = (x1+x2) / (n1 + n2)
= (41+25) / ( 423+294)
= 0.092
1=x1/n1=0.097
2=x2/n2=0.085
#Critical value =-zα=-Z0.10=-1.2815
Test statistics
Z = (1 - 2) / sqrt [ p ( 1 -p) * ( 1 / n 1+ 1 / n2) ]
= ( 0.097- 0.085) / sqrt ( 0.092( 1 - 0.092) * ( 1 / 423 + 1 / 294) )
=0.542
#Critical regeion is
reject Ho if z<-zα
here z> -zα ie 0.542>-1.28
hencewe fail to Reject H0 .
This test statistic leads to a decision to...
fail to reject the null
#Conclusion:
There is sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion.
You wish to test the following claim (H1) at a significance level of α=0.10. Ho:p1=p2 H1:p1<p2...
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