Question

A researcher is interested in whether people who write with the left hand have a greater gripping strength in their left hand than their right hand. They state their hypotheses:

H0 : The mean difference in left and right hand strengths is zero

HA : The mean difference in left and right hand strengths (L-R) is positive

The left- and right-hand gripping strengths of 10 randomly selected left-handed writers are measured and recorded:

Person	1	2	3	4	5	6	7	8	9	10	Mean	Sample SD
Left Hand	140	90	125	129	95	121	85	97	131	110	112.3	19.48
Right Hand	138	87	110	131	96	120	86	90	129	100	108.7	19.64

(a) Explain why it would be inappropriate to perform a two sample hypothesis test based on the data collection

(b) Compute the appropriate test statistic, degrees of freedom, if relevant, and p value for the hypotheses. (Show your work) (Assume the population of differences is approximately normal)

Answer 1

L	R	d=L-R	(d-dbar)
140 90 125 129 95 121 85 97 131 110	138 87 110 131 96 120 86 90 129 100	2 3 15 -2 -1 1 -1 7 2 10 M: 3.6	2.56 0.36 129.96 31.36 21.16 6.76 21.16 11.56 2.56 40.96 S: 268.4