HP HP-11C - Page 179

Section 10: Applications Programs 177
The test statistic
D
t=
vn
$p
which has n — 1 degrees of freedom (df) can be used to test the null
hypothesis, Hy: u; = po.
t Statistic for Two Means
Suppose {x{, xo, ..., Xp,} and {yy, y9, ..., Yn,} are independent random
samples from two normal populations having means u; and us
(unknown) and the same unknown variance o2
We want to test the null hypothesis Hy: u; — ug =d.
Equations:
ny
_ 1 E
X = X;
ny =
ng
_ 1
y= Yi
ny 4
X —y—d
t= Y
/ 1 4 1 Jixl‘2_n1i2+xyi2—n25’2
V n; no n, + ny — 2
We can use this t statistic (which has the t distribution with n; + n,
— 2 degrees of freedom (df)) to test the null hypothesis H,.
References:
1. Statistics in Research, B. Ostle, lowa State University Press,
1963.
2. Statistical Theory and Methodology in Science and Engi-
neering, K.A. Brownlee, John Wiley and Sons, 1965.