How hard is it to maintain your balance while you are concentrating? Nine elderl

Question

How hard is it to maintain your balance while you are concentrating? Nine elderly people (6 men and 3 women) and eight young men were subjects in this experiment. Each subject stood barefoot on a force platform and was asked to maintain a stable upright position and to react as quickly as possible to an unpredictable noise by pressing a hand-held button. The noise came randomly, and the subject concentrated on reacting as quickly as possible. The platform automatically measured how much each subject swayed in millimeters. Test whether there is any difference between the two age groups in the amount that they swayed in reacting to the noise. The measurement of subject 19 may be an outlier. How would removing that one measurement affect the outcome of the test?

Explanation / Answer

Part-A

From following results we observe that we have at 0.05 level enough evidence to reject the null hypothesis as t(15)=2.20 with p-value=0.044<0.05. Hence, there is difference between the two age groups in the amount that they swayed in reacting to noise.

Two-Sample T-Test and CI: Sway, Age Group

Two-sample T for Sway

Age Group N Mean StDev SE Mean
elderly 9 26.33 9.77 3.3
young 8 18.13 4.09 1.4

Difference = (elderly) - (young)
Estimate for difference: 8.21
95% CI for difference: (0.27, 16.15)
T-Test of difference = 0 (vs ): T-Value = 2.20 P-Value = 0.044 DF = 15
Both use Pooled StDev = 7.6632

Part-B

After removing the measurement of subject 19 we get the results as follows from where we observe that we have at 0.05 level enough evidence to reject the null hypothesis as t(14)=2.48 with p-value=0.026<0.05. Hence, there is difference between the two age groups in the amount that they swayed in reacting to noise even after removing the outlier. However, the p-value is decreaed

Two-Sample T-Test and CI: Sway, Age Group

Two-sample T for Sway

Age Group N Mean StDev SE Mean
elderly 8 23.38 4.37 1.5
young 8 18.13 4.09 1.4

Difference = (elderly) - (young)
Estimate for difference: 5.25
95% CI for difference: (0.71, 9.79)
T-Test of difference = 0 (vs ): T-Value = 2.48 P-Value = 0.026 DF = 14
Both use Pooled StDev = 4.2321

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