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AP Statistics 4.9 A Identify an Appropriate Testing Method for the Difference Between Two Population Means Including the Parameters Questions

Identify a two-sample t-test for independent groups and define the population mean difference, response variable, and populations.

Syllabus
Effective Fall 2026
Course
AP Statistics

Exam points

  • choose a two-sample t-test when independent groups provide quantitative response measurements
  • distinguish independent groups from matched or naturally paired observations requiring a paired t-test

AP Statistics 4.9 A Identify an Appropriate Testing Method for the Difference Between Two Population Means Including the Parameters Questions question 1

Stefan, a psychologist, conducted a study to investigate the effect of time of day on reading comprehension in children. One hundred children volunteered, with their parents' consent, to participate in the study. Fifty of the children were randomly assigned to read a story at 9 a.m.

and then answer 25 questions about it. The remaining 50 children were assigned to read the same story at 3 p.m. and answer the same 25 questions. The reading comprehension for each child was measured by a reading score, which was determined by the number of questions that were answered correctly about the story. Stefan is interested in comparing the mean reading scores for the two times of day. Table 1 shows the results of Stefan's study.

Table 1: Summary Statistics of Reading Scores

Table 1: Summary Statistics of Reading Scores

Stefan found the conditions for inference were met and conducted a two-sample t-test for the difference in two population means. Let μAM\mu_{\mathrm{AM}} represent the mean reading score for all children, similar to those in the study, who would read the story at 9 a.m. Let μPM\mu_{\mathrm{PM}} represent the mean reading score for all children, similar to those in the study, who would read the story at 3 p.m.

Stefan's hypotheses are as shown.

H0:μAM=μPMHa:μAM≠μPM\begin{aligned} & \mathrm{H}_{0}: \mu_{\mathrm{AM}}=\mu_{\mathrm{PM}} \\ & \mathrm{H}_{\mathrm{a}}: \mu_{\mathrm{AM}} \neq \mu_{\mathrm{PM}} \end{aligned}

Explain why it was appropriate for Stefan to conduct a two-sample t-test for the difference in two population means instead of a paired t-test for the population mean difference.

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