• Complete a two-sample [latex]t[/latex]-test for dependent population means from hypotheses to conclusions

Differences in Reaction Times

In a hypothesis test for matched or paired samples, subjects are matched in pairs, and differences are calculated. Let’s calculate the point estimate of the mean of differences between two paired samples. That is, let’s calculate the difference between the reaction time of each participant with the use of a cell phone and without the use of a cell phone.

The difference is defined by:

Difference = (reaction time with the use of a cell phone) – (reaction time without the use of a cell phone)

Let’s calculate the sample mean difference and the sample standard deviation of the differences using our statistical tool.

Under “Enter Data”, select “Your Own”. Copy and paste the following difference data.

Difference Column

Difference
32
67
75
150
142
56
29
84
-13
-11
10
22
-24
29
19
87
101
-7
45
-2
66
73
10
148
8
130
90
146
39
20
6
-7

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The mean of the differences is equal to the difference in means.

[latex]\mu_d = \mu_\text{with cell phone}-\mu_\text{without cell phone}[/latex]