Concluding a Test for a Population Proportion Practice

Sample questions

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1. Sample 1difficulty 2/5

   Test H₀: p = 0.25 vs Hₐ: p ≠ 0.25, with n=400, p̂ = 0.30.

   The test statistic is approximately:

   • A

     2.31

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   • B

     1.96

   • C

     1.15

   • D

     0.05

   Why

   z ≈ 0.05/0.02165 ≈ 2.31.

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2. Sample 2difficulty 2/5

   A test of H₀: p = 0.4 vs Hₐ: p ≠ 0.4 yields p-value = 0.08 with α = 0.05.

   Which conclusion is appropriate?

   • A

     Accept H₀; p equals 0.4.

   • B

     Fail to reject H₀; insufficient evidence that p ≠ 0.4.

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   • C

     Cannot determine without more data.

   • D

     Reject H₀; convincing evidence that p ≠ 0.4.

   Why

   Since 0.08 > 0.05, fail to reject H₀. There is not convincing evidence that p ≠ 0.4.

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3. Sample 3difficulty 2/5

   A z-test of H₀: p = 0.5 vs Hₐ: p > 0.5 produces p-value = 0.012. Significance level α = 0.05.

   What is the correct decision and conclusion?

   • A

     Accept H₀; the proportion equals 0.5.

   • B

     Reject H₀; there is convincing evidence p > 0.5.

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   • C

     Reject Hₐ; the data support H₀.

   • D

     Fail to reject H₀; not enough evidence.

   Why

   Since p-value (0.012) < α (0.05), reject H₀. There is convincing evidence that p > 0.5.

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4. Sample 4difficulty 3/5

   Output for a one-proportion z-test of H₀: p = 0.50 vs Hₐ: p > 0.50.

   At α = 0.05, the conclusion is:

   • A

     Accept H₀.

   • B

     Fail to reject H₀.

   • C

     Insufficient data.

   • D

     Reject H₀; convincing evidence p > 0.50.

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   Why

   P-value 0.0139 < 0.05, so reject H₀; there is convincing evidence p > 0.50.

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