Everyone has a dominant hand, or a hand that is used more often than the other o

Question

Everyone has a dominant hand, or a hand that is used more often than the other one. So it is reasonable to think then that someone’s dominant hand might have a better (quicker) reaction time than that same person’s non-dominant hand. I went to 7 people and recorded their reaction speed (the amount of time it takes someone to react to a change in color, recorded in milliseconds) for both their dominant and non-dominant hands. Conduct a hypothesis test at the 5% level of significance to see if there is some difference between dominant and non-dominant hand reaction speeds. Also, construct a 95% confidence interval for the true mean difference in reaction speeds between someone’s dominant and non-dominant hands. (do not forget to do both the hypothesis test and confidence interval) Person Dominant Hand Reaction Speed (in ms) Non-Dominant Hand Reaction Speed (in ms) 1. 164 178 2. 227 243 3. 231 235 4. 195 191 5. 177 212 6. 296 254 7. 240 272

164, 227, 231, 195, 177, 296, 240 are for dominant hand reaction speed (in ms)

178, 243, 235, 191, 212, 254, 272 are for non-dominant hand reaction speed (in ms)

Explanation / Answer

Solution:

First of all, we have to conduct a paired t test for checking the hypothesis whether there is any significant difference in the average dominant and non-dominant hand reaction time or not. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: There is no any significant difference in the average dominant and non-dominant hand reaction time.

Alternative hypothesis: Ha: There is a significant difference in the average dominant and non-dominant hand reaction time.

This is a two tailed test. The level of significance or alpha value for this test is given as 0.05 or 5%.

The test statistic formula for this test is given as below:

Test statistic = t = Dbar / [SD/sqrt(n)]

Where SD is the standard deviation of difference

Calculations for this test statistic are given as below:

Sample size = n = 7

Degrees of freedom = n – 1 = 7 – 1 = 6

X

Y

Di

(Di - DBar)^2

164

178

-14

37.73469388

227

243

-16

66.30612245

231

235

-4

14.87755102

195

191

4

140.5918367

177

212

-35

736.7346939

296

254

42

2485.734694

240

272

-32

582.877551

Dbar = -7.85714

SD = 26.0284

t = -7.85714 / (26.0284/sqrt(7)) = -0.79866755

P-value = 0.4549 (By using t-table)

Alpha value = 0.05

P-value > Alpha value

So, we do not reject the null hypothesis that there is no any significant difference in the average dominant and non-dominant hand reaction time.

There is no sufficient evidence of significant difference in the average dominant and non-dominant hand reaction time.

Now, we have to find out the 95% confidence interval for the mean difference in reaction times. The confidence interval formula is given as below:

Confidence interval = Dbar -/+ t*SD/sqrt(n)

Critical t value for 95% confidence level and df = 6 is given as 2.4469.

Confidence interval = -7.85714 -/+ 2.4469*(26.0284/sqrt(7))

Lower limit = -7.85714 - 2.4469*(26.0284/sqrt(7)) = -31.92927849

Upper limit = -7.85714 + 2.4469*(26.0284/sqrt(7)) = 16.21499849

Confidence interval = (-31.93, 16.21)

The mean difference 0 is lies between the above confidence interval so we do not reject the null hypothesis that there is no any significant difference in the average dominant and non-dominant hand reaction time.

X

Y

Di

(Di - DBar)^2

164

178

-14

37.73469388

227

243

-16

66.30612245

231

235

-4

14.87755102

195

191

4

140.5918367

177

212

-35

736.7346939

296

254

42

2485.734694

240

272

-32

582.877551

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