Question

First sample average = 4 Second sample average = 9 SS for first sample = 16 SS for second sample = 15 Sample size for first sample = 8 Sample size for second sample = 8 Compute the t-score. Round your answers to 2 decimal places and be sure to include the negative (-) if necessary, in your answer. Enter your response in the space provided here.

Answer 1

1st sample average ($\bar{X1}$) = 4

2nd sample average ($\bar{X2}$) = 9

SS for 1st sample = 16

SS for 2nd sample = 15

n1 = 8 ( sample size of 1st sample)

n2 = 8 (sample size of 2nd sample)

Variance of 1st sample (s1^{​​​​​2}​) = (SS for 1st sample/n1)=(16/8) = 2

Variance of 2nd sample (s2^{​​​​​2}​) = (SS for 2nd sample/n2)=(15/8) = 1.875

Pooled variance (s^{​​​​​​2}​​​​​) =((n1-1)*s1^{​​​​​2} + (n2 -1)*s2^{​​​​​2}​)/(n1+n2-2)

= (7*2 + 7*1.875)/(8+8-2) = 1.9375

So, s = $\sqrt{s^{2}}$ = 1.3919

Therefore t-score = ($\bar{X1}$ - $\bar{X2}$ )/s = (4-9)/1.3919*0.5 = -7.18

Vnit n2

Answer : t-score = -7.18