Question

he weights of randomly selected 5 female students and 5 male students are given by the following:weights for male students:160,165,152,158,178weights for female students:169,154,158,156,162.

Let the weight distributions of male and female students follow N(μ1,σ1) and N(μ2,σ2)respectively.

Find the correlation coefficient between the heights of male and female students.(5 points)

Answer 1

The provided data are shown in the table below

X	Y
160	169
165	154
152	158
158	156
178	162

Also, the following calculations are needed to compute the correlation coefficient:

	X	Y	X*Y	X2	Y2
	160	169	27040	25600	28561
	165	154	25410	27225	23716
	152	158	24016	23104	24964
	158	156	24648	24964	24336
	178	162	28836	31684	26244
Sum =	813	799	129950	132577	127821

The correlation coefficient r is computed using the following expression:

where

In this case, based on the data provided, we get that

Therefore, based on this information, the sample correlation coefficient is computed as follows

which completes the calculation.