Question

You wish to test the following claim (HaHa) at a significance level of α=0.02α=0.02.

      Ho:p1=p2Ho:p1=p2
      Ha:p1≠p2Ha:p1≠p2

You obtain 412 successes in a sample of size n1=655n1=655 from the first population. You obtain 416 successes in a sample of size n2=731n2=731 from the second population. Use the normal distribution as an approximation for the binomial distribution.

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

Answer 1

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 412 + 416 ) / ( 655 + 731 )
= 0.5974

Z = 2.270

Test Criteria :-
Reject null hypothesis if

Critical value   

= 2.27 < 2.33, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = 2 * P ( Z < 2.27 )
P value = 0.0232
Reject null hypothesis if P value <
Since P value = 0.0232 > 0.02, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0