Question

A sample of 90 observations indicated that X₁ is 62. A second sample of 146 observations indicated that X₂ is 93. Conduct a z-test of hypothesis about a difference in population proportions using a 0.04 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 less than -2.05 or greater than 2.05.
	Reject H0 in favour of H1 if the computed value of the statistic is between -2.05 and 2.05.
	Reject H0 in favour of H1 if the computed value of the statistic is less than -1.75.
	Reject H0 in favour of H1 if the computed value of the statistic is between -1.75 and 1.75.
	Reject H0 in favour of H1 if the computed value of the statistic is less than -1.75 or greater than 1.75.
	Reject H0 in favour of H1 if the computed value of the statistic is greater than 2.05.
	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: 0

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: 0

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

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