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AP Statistics 4.10.A Calculating Two-Sample t Tests

Practise calculating two-sample t-statistics and p-values from independent sample summaries, with tail direction matched to the alternative hypothesis.

Syllabus
Effective Fall 2026
Course
AP Statistics

Exam points

  • Calculate t from the ordered sample-mean difference divided by sqrt(s1 squared/n1 + s2 squared/n2).
  • Use a one- or two-sided t tail that matches the alternative hypothesis to obtain the p-value.
  • Compare the p-value with alpha and state the evidence about the ordered population means in context.

4.10.A—Calculate an appropriate test statistic and p-value for testing a hypothesis for the difference between two… question 1

[Maximum number: 5]

An experiment is run to test whether daily stimulation of specific reflexes in young infants will lead to earlier walking. Twenty infants were recruited through a pediatrician's service and were randomly split into 2 groups of 10 . One group received the daily stimulation, while the other was considered a control group. The ages (in months) at which the infants first walked alone were recorded.

With stimulation: 10,12,11,10.5,11,11.5,11.5,11,12,11.5Mean=11.2,SD=0.6324610,12,11,10.5,11,11.5,11.5,11,12,11.5 \quad \mathrm{Mean}=11.2, \mathrm{SD}=0.63246
Control: 10, 13, 12, 11, 11.5, 11.5, 12.5, 12, 11.5, 1111 \quad Mean = 11.6, SD=0.84327\mathrm{SD}=0.84327

Figure for Question 4.10.A—Calculate an appropriate test statistic and p-value for testing a hypothesis for the difference between two… question 1 — AP Statistics

Complete the inference procedure, including calculations.

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