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 45.2% successes in a sample of size n1=389n1=389 from the first population. You obtain 51.4% successes in a sample of size n2=578n2=578 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

As we are testing here for the equality of proportions, the pooled proportion here is computed as:

The standard error now is computed here as:

The test statistic now is computed here as:

Therefore -1.891 is the required test statistic value here.

b) As this is a two tailed test, the p-value here is computed from the standard normal tables as:

p = 2P(Z < -1.891) = 2*0.0293 = 0.0586

Therefore 0.0586 is the required p-value here.

c) The p-value here is 0.0586 > 0.02 which is the level of significance.

d) As the p-value is higher than the level of significance, therefore the test is not significant. we cannot reject the null hypothesis here.

e) There is not sufficient sample evidence to support the claim that the first population proportion is not equal to the second population proportion.