Is there a significant difference between the two populations represented by these two samples? Use a two-tailed test with α = .01 (t critical = +/- 2.75)

Question

n1=18, M1=42, SS1=398

n2=16, M2=48.6, SS2=370

Answer 1

Since the samples are from two populations, I would not assume the variances to be equal. I'll include this calculation if there's a note to allow for equal variances.

Unequal variances

s₁² = 398/17 = 23.412

s₂² = 370/15 = 24.667

t = (M₁ - M₂) / sqrt(s₁²/18 + s₁²/16)

= -6.6/1.686 = -3.915

Because this t statistic is outside of the critical bounds (less than -2.75), we have sufficient evidence to say that the means of the populations are different.

Equal variances

s_p² = (SS₁ + SS₂) / (18+16-2)

= 24

t = (M₁ - M₂) / sqrt(s_p²•(1/18 + 1/16))

= -6.6/1.683 = -3.921

This calculation generates the same conclusion

Thus, we can conclude that there is sufficient evidence that the means of the two populations are different.