AP Statistics 4.9.C Conditions for Two-Sample t-Tests

Practise justifying a two-sample t-test by checking independent random groups and assessing small-sample distributions for skewness and outliers.

Exam points

Check randomization and independence between groups; nonrandom samples prevent population inference.
With small samples, inspect both group distributions for approximate normality, strong skewness, and outliers.

[Maximum number: 1]

A college admissions officer is interested in comparing the SAT Math scores of high school applicants who have and have not taken AP Statistics. She randomly pulls the files of five applicants who took AP Statistics and five applicants who did not, and proceeds to run a t-test to compare the mean SAT Math scores of the two groups. Which of the following is a necessary assumption?

The population variances from each group are known.

The population variances from the two groups are equal.

The population of all SAT scores from each group is roughly normally distributed.

The samples must be independent simple random samples, and for each sample, n p and n(1-p) must both be at least 10 .

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4.9.C—Justify the appropriateness of a hypothesis test for the difference between two population means by verifying… question 1