Measurements of the right-hand and left-hand gripping strengths of six people ar

Question

Measurements of the right-hand and left-hand gripping strengths of six people are measured. The data are shown in the table below with some summary statistics: (a) We would like to conduct inference procedures to estimate and test for the mean difference in right-hand and left-hand gripping strengths. What assumptions are necessary? (b) Assuming all appropriate assumptions are satisfied, calculate a 95% confidence interval for the true mean difference in gripping strength between people's right and left hands. (c) Provide an interpretation of the confidence interval in (b).

Explanation / Answer

Solution:

a. The necessary observations are:-

i. The dependent variable should be approximately normally distributed.

ii. The observations are independent of one another.

iii. The dependent variable must be continuous

b. X-barD = 5 and sD = 6

Degrees of freedom, df = n – 1 = 6 – 1 = 5

Using t-tables, the critical value is

t (0.05/2, 5) = t (0.025, 5) = 2.571

95% confidence interval is given by:-

X-barD ± t*sD/n

5 ±2.571*6/5

5 ± 2.571*2.683

5 ± 6.90

-1.9, 11.90

c. We are 95% confident that the true mean difference in gripping strength between people’s right and left hands lies within -1.9, 11.9.

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