Sample 1: mean 24.0 cm, s = 3.0 cm, n = 9. Sample 2: mean 20.0 cm, s = 4.0 cm, n = 16. The critical value of t at p = 0.05 for these samples is 2.07. Is the difference between the means significant?
- s12/n1 = 9.0 ÷ 9 = 1.0 and s22/n2 = 16.0 ÷ 16 = 1.0.
- √(1.0 + 1.0) = √2.0 = 1.41.
- t = (24.0 − 20.0) ÷ 1.41 = 2.83.
- Degrees of freedom = 9 + 16 − 2 = 23, and 2.83 is greater than 2.07.
Answer: t = 2.83, so the difference between the means is significant at p = 0.05.