AP Statistics 4.10 A Calculate an Appropriate Test Statistic and P Value for Testing a Hypothesis for the Difference Between Two Questions

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

Exam points

calculate t from the ordered sample-mean difference divided by sqrt(s1 squared/n1 plus s2 squared/n2)
use a one- or two-sided t tail that matches the alternative hypothesis to obtain the p-value

[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: $10,12,11,10.5,11,11.5,11.5,11,12,11.5 \quad \mathrm{Mean}=11.2, \mathrm{SD}=0.63246$
Control: 10, 13, 12, 11, 11.5, 11.5, 12.5, 12, 11.5, $11 \quad$ Mean = 11.6, $\mathrm{SD}=0.84327$

Figure for Question AP Statistics 4.10 A Calculate an Appropriate Test Statistic and P Value for Testing a Hypothesis for the Difference Between Two Questions question 1 — AP Statistics

Complete the inference procedure, including calculations.

Let $\mu_1$ and $\mu_2$ be the true mean walking ages for infants receiving stimulation and no stimulation. Test $H_0:\mu_1=\mu_2$ against $H_a:\mu_1<\mu_2$ . Random assignment satisfies randomization;
the dotplots show no outliers or strong skew, supporting normality. The test gives t=-1.20, df=16.69, and p=0.1234.

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AP Statistics 4.10 A Calculate an Appropriate Test Statistic and P Value for Testing a Hypothesis for the Difference Between Two Questions question 1