Question

You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01.

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

You obtain a sample from the first population with 294 successes and 167 failures. You obtain a sample from the second population with 402 successes and 200 failures. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

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

	Pop 1	Pop 2
x=	294	402
n =	461	602
p̂=x/n=	0.6377	0.6678
estimated prop. diff =p̂1-p̂2    =		-0.0300
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.6548
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0294
test stat z=(p̂1-p̂2)/Se =		-1.021

P value   =

0.1537

(from excel:1*normsdist(-1.02)

the p value is less than α

This test statistic leads to a decision to fail to reject the null

There is not sufficient sample evidence to support the claim that the first population proportion is less than the second population proportion.