9
QuizMultiple Choice

Preparing to Test a Claim about a Population Proportion

Question 9 • AQR_A_IC

It is claimed that 95% of teenagers who have a cell phone never leave home without it. To investigate this claim, a random sample of 300 teenagers who have a cell phone was selected. It was discovered that 273 of the teenagers in the sample never leave home without their cell phone. One question of interest is whether the data provide convincing evidence that the true proportion of teenagers who never leave home without a cell phone is less than 95%. What are the values of the test statistic and P-value for this test?Find the z-table here.

Answer
A
z = 3.18, P-value = 0.0007
B
z = –3.18, P-value = 0.0007
C
z = 3.18, P-value = 0.0014
D
z = –3.18, P-value = 0.0014

Explanation

The sample proportion is 273/300 = 0.91. Under the claim p = 0.95, the standard error is √(0.95 × 0.05/300) ≈ 0.0126, so z = (0.91 − 0.95)/0.0126 ≈ −3.18. Because the alternative is that the true proportion is less than 95%, use the lower-tail probability; for z = −3.18, the P-value is about 0.0007. Thus, the correct choice is z = −3.18 and P-value = 0.0007.

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