Question

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

      Ho: p1 = p2
      Ha: p1 ≠ p2

You obtain 49.1% successes in a sample of size n1=689 from the first population. You obtain 57.7% successes in a sample of size n2=691 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 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 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

The statistical software output for this problem is :

Test statistics = -3.202

P-value = 0.0014

The p-value is less than (or equal to) α

reject the null

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