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AP Statistics 4.6 B Justify the Appropriateness of Conditions for the Sampling Distribution of the Difference Between Two Sample Means Questions

Practise justifying the normal model for a difference in sample means by checking that both independent samples are sufficiently large.

Syllabus
Effective Fall 2026
Course
AP Statistics

Exam points

  • Use n1 at least 30 and n2 at least 30 to justify an approximately normal model for x-bar1 minus x-bar2.

AP Statistics 4.6 B Justify the Appropriateness of Conditions for the Sampling Distribution of the Difference Between Two Sample Means Questions question 1

[Maximum number: 1]

Researchers surveyed a random sample of 55 adults in neighborhood A and 64 adults in neighborhood B from populations of over 1,000 adults in each neighborhood. The sampled individuals were asked what their families anticipated spending on Halloween. Let xˉA\bar{x}_{A} be the calculated mean spending of the 55 adults in neighborhood A, and let xˉB\bar{x}_{B} be the calculated mean spending of the 64 adults in neighborhood B. Which of the following is the best explanation for why the sampling distribution of xˉA−xˉB\bar{x}_{A}-\bar{x}_{B} can be modeled with a normal distribution?

A

There are at least 30 people in each population.

B

The sample sizes are sufficiently large.

C

The population distributions are assumed to be roughly normal.

D

The sample distributions are assumed to be unimodal and roughly symmetric.

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