Question

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...

• in the critical region
• not in the critical region

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion.
• There is not sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion.
• The sample data support the claim that the first population proportion is less than the second population proportion.
• There is not sufficient sample evidence to support the claim that the first population proportion is less than the second population proportion.

Answer 1

Null and

Ho:p1=p2
      H1:p1<p2

Pooled proportion=p = (x1+x2) / (n1 + n2)

= (41+25) / ( 423+294)

= 0.092

$\hat{p}$1=x1/n1=0.097

$\hat{p}$2=x2/n2=0.085

#Critical value =-zα=-Z0.10=-1.2815

Test statistics

Z = ($\hat{p}$1 - $\hat{p}$ 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.