Question

A sample of 112 observations indicated that X₁ is 100. A second sample of 146 observations indicated that X₂ is 97. 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. Reject H0 in favour of H1 if the computed value of the statistic is greater than 2.05. 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 between -1.75 and 1.75. 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. 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

hypothesis:-

a).the decision rule be:-

Reject H₀ in favor of H₁ if the computed value of the statistic is less than -2.05 or greater than 2.05.

[z critical value for 0.04 level of significance = 2.05

steps:-

in any blank cell of excel type =NORMSINV(0.04/2)..then press enter. you will get -2.05375

just take the absolute value. ]

given data and some necessary calculations are:-

b). the pooled proportion be:-

c).the value of the test statistic be:-

  

d).the decision regarding H_0:-

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.

[ z calculated = 4.281 > 2.05

so, we reject the null hypothesis. ]

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