A study of the effects of exercise used rats bred to have high or low capacity for exercise. The 8 high-capacity rats had mean blood pressure 89 mm Hg and variance 81 (mm Hg)'; the 8 low-capacity rats had mean blood pressure 105 mm Hg with variance 169 (mm Hg). What is the value of the two-sample t statistic for comparing the two population means

T statistic = 0.256

Step-by-step explanation:

Given :

High capacity rats:

nh = 8

Xh = 89

s²h = 81

Low capacity rats :

nl = 8

Xl = 105

s²l = 169

Test statistic :

(Xh - Xl) ÷ Sp(sqrt(1/nh + 1/nl))

Pooled variance (Sp) :

[(nh - 1)s²h + (nl - 1)s²l] ÷ (nh + nl - 2)

[(8 - 1)*81 + (8 - 1)*169] ÷ (8 + 8 - 2)

(7*81 + 7*169) ÷ 14

= 1750 / 14

= 125

Hence,

(89 - 105) ÷ 125(sqrt[1/8 + 1/8)

16 ÷ (125 * 0.5)

16 /62.5

= 0.256