Question

You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10.

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

You obtain a sample from the first population with 153 successes and 596 failures. You obtain a sample from the second population with 71 successes and 174 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

The sample proportions here are computed as:

p₁ = 153 / (153+596) = 0.2043
p₂ = 71 / (174+71) = 0.2898

The pooled proportion here is computed as:

P = (153+71) / (749+245) = 0.2254

The standard error here is computed as:

The test statistic here is computed as:

Therefore -2.781 is the test statistic value here.

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

p = P(Z <- 2.781 ) = 0.0027

Therefore 0.00027 is the p-value here.

Clearly the p-value here is 0.0027 less than 0.10 which is

Therefore the test is significant and

The null hypothesis is  rejected here.

#Conclusion

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