Question

You wish to test the following claim (Ha) at a significance level of α=0.001.

      Ho: p1 = p2
      Ha: p1 ≠ p2

You obtain 656 successes in a sample of size n1=773 from the first population. You obtain 203 successes in a sample of size n2=255 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

Solution :

Given that,

n₁ = 773

x₁ = 656

  ₁ = 0.84864165588

n₂ =255

x₂ = 203

  ₂ = 0.79607843137

Let be the pooled proportion.

= (x1 +x2)/(n1 + n2) = 0.83560311284

1 - = 1 - 0.83560311284 = 0.16439688716

Q . What is the test statistic for this sample?

The test statistic z is

z =  

    = (0.84864165588 - 0.79607843137)/[0.83560311284*0.16439688716*((1/773)+(1/255))]

= 1.964

test statistic = 1.964

Q . What is the p-value for this sample?

sign in H1 indicates that the test id "Two Tailed"

p value = 2 * P(Z < -z)

= 2 * P(Z < -1.964)

= 2 * 0.0248

= 0.0496

p-value = 0.0496

The p-value is...

greater than α

This test statistic leads to a decision to...

fail to reject the null

As such, the final conclusion is that...

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