Question 2

A sample of 91 observations indicated that X₁is 70. A second sample of 140 observations indicated that X₂is 89. Conduct az-test of hypothesis about a difference in population proportions using a 0.05 significance level.

H₀: p₁- p₂= 0

H₁: p₁- p₂ 0

a)State the decision rule.

a. RejectH₀in favour ofH₁if the computed value of the statistic is less than 1.96.

b. RejectH₀in favour ofH₁if the computed value of the statistic is greater than 1.96.

c. RejectH₀in favour ofH₁if the computed value of the statistic is less than -1.64 or greater than 1.64.

d. RejectH₀in favour ofH₁if the computed value of the statistic is between -1.64 and 1.64.

e. RejectH₀in favour ofH₁if the computed value of the statistic is less than -1.96 or greater than 1.96.

f. RejectH₀in favour ofH₁if the computed value of the statistic is between -1.96 and 1.96.

g. 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 regardingH₀?

a. There is sufficient evidence, at the given significance level, to rejectH₀, and acceptH₁or at least there is not enough evidence to rejectH₁.

b. There is insufficient evidence, at the given significance level, to rejectH₀.

c. There is insufficient evidence to reject or not reject the null hypothesis.