AP Statistics 4.6.B Conditions for Two Sample Means

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

Exam points

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

[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 $\bar{x}_{A}$ be the calculated mean spending of the 55 adults in neighborhood A, and let $\bar{x}_{B}$ 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 $\bar{x}_{A}-\bar{x}_{B}$ can be modeled with a normal distribution?

There are at least 30 people in each population.

The sample sizes are sufficiently large.

The population distributions are assumed to be roughly normal.

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

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4.6.B—Justify the appropriateness of conditions for the sampling distribution of the difference between two sample means question 1