Question

You wish to test the following claim (H1H1) at a significance level of α=0.02α=0.02.

      Ho:p1=p2Ho:p1=p2
      H1:p1>p2H1:p1>p2

You obtain 113 successes in a sample of size n1=450n1=450 from the first population. You obtain 91 successes in a sample of size n2=399n2=399 from the second population. 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 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 greater than the second population proportion.
• There is not sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion.
• The sample data support the claim that the first population proportion is greater than the second population proportion.
• There is not sufficient sample evidence to support the claim that the first population proportion is greater than the second population proportion.

Answer 1

Here we have given that,

Claim: To check whether the first population proportion is greater than the second population proportion.

The null and alternative hypotheses is as follows,

Ho: P1=P2

v/s

H1:P1 > P2

we have given that,

n1= 1st Sample size from first population =450

x1=number of success from the first sample=113

n2= 2nd Sample size from second population=399

x2=number of success from the second sample=91

Now we estimate the proportion p as

=1st sample proportion =

= 2nd sample proportion =

We are using the 2 sample proportion test and normal distribution as an approximation for the binomial distribution.

Now, we can find the critical value.

= level of significance= 0.02

This is right-tailed test.

Z-critical =2.05 Using EXCEL software = NORMSINV(probablity=0.02)

Now, we can find the test statistics for sample

=

=0.786

The test statistics for this sample is 0.786

Decision:

Z-statistics (0.786) < Z-critical (2.05)

The test statistics is not in the critical region.

Conclusion:

We fail to reject null hypothesis Ho.

There is not sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion.