Question

A sample of 104 observations indicated that X₁ is 80. A second sample of 141 observations indicated that X₂ is 106. Conduct a z-test of hypothesis about a difference in population proportions using a 0.01 significance level.

    H₀: p₁ - p₂ = 0
    H₁: p₁ - p₂ ≠ 0

a)State the decision rule.Reject H₀ in favour of H₁ if the computed value of the statistic is between -2.58 and 2.58.Reject H₀ in favour of H₁ if the computed value of the statistic is less than 2.58.Reject H₀ in favour of H₁ if the computed value of the statistic is greater than 2.58.Reject H₀ in favour of H₁ if the computed value of the statistic is less than -2.33 or greater than 2.33.Reject H₀ in favour of H₁ if the computed value of the statistic is between -2.33 and 2.33.Reject H₀ in favour of H₁ if the computed value of the statistic is less than -2.58 or greater than 2.58.None of the above.
b) Compute the pooled proportion.
For full marks your answer should be accurate to at least four decimal places.

Pooled proportion: 

c) What is the value of the test statistic?
For full marks your answer should be accurate to at least three decimal places.

Test statistic: 

d)What is your decision regarding H₀?There is sufficient evidence, at the given significance level, to reject H₀, and accept H₁ or at least there is not enough evidence to reject H₁.There is insufficient evidence, at the given significance level, to reject H₀.There is insufficient evidence to reject or not reject the null hypothesis.

Answer 1