Preparing to Test a Claim about a Population Proportion
Question 2 • AQR_A_IC
According to historical data, it is believed that 12% of American adults work more than one job. To investigate if this claim is still accurate, a random sample of 100 American adults is selected. It is discovered that 18 of them work more than one job. A researcher would like to know if the data provide convincing evidence that the true proportion of American adults who work more than one job differs from 12%. What are the values of the test statistic and P-value for this test?Find the z-table here.
Answer
A
z = 1.85, P-value = 0.0322
B
z = –1.85, P-value = 0.0322
C
z = 1.85, P-value = 0.0644
D
z = –1.85, P-value = 0.0644
Explanation
Under the null hypothesis, the sample proportion is expected to be 0.12, with standard error √(0.12 × 0.88 ÷ 100) ≈ 0.0325. The observed proportion is 18 ÷ 100 = 0.18, so the test statistic is z = (0.18 − 0.12) ÷ 0.0325 ≈ 1.85. Because the question asks whether the proportion differs from 12%, the test is two-sided; the P-value is about 2 × 0.0322 = 0.0644. The correct choice is C, z = 1.85 and P-value = 0.0644.
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