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AP Statistics 3.3 B Justify the Appropriateness of Constructing a Confidence Interval for a Population Proportion By Verifying Questions

Practise justifying a one-proportion z-interval by verifying random selection, population size relative to the sample, and sufficient observed successes and failures.

Syllabus
Effective Fall 2026
Course
AP Statistics

Exam points

  • verify that the data come from a random sample or another random selection process
  • check that sampling without replacement uses no more than ten percent of the population
  • check at least ten observed successes and failures and link the condition to normal approximation

AP Statistics 3.3 B Justify the Appropriateness of Constructing a Confidence Interval for a Population Proportion By Verifying Questions question 1

A polling agency showed the following two statements to a random sample of 1,048 adults in the United States.

Environment statement: Protection of the environment should be given priority over economic growth.
Economy statement: Economic growth should be given priority over protection of the environment.

The order in which the statements were shown was randomly selected for each person in the sample. After reading the statements, each person was asked to choose the statement that was most consistent with his or her opinion. The results are shown in the table.

Table for Question AP Statistics 3.3 B Justify the Appropriateness of Constructing a Confidence Interval for a Population Proportion By Verifying Questions question 1 — AP Statistics

One of the conditions for inference that was met is that the number who chose the economy statement and the number who did not choose the economy statement are both greater than 10. Explain why it is necessary to satisfy that condition.

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