HP -11C Owner's Handbook Manual page 90

176 Section 10: Applications Programs
Keystrokes Display
25.6 [ENTER] 25.60
32.8 [ENTER 32.80
42.3{E] 410.85 Area.
(R7S) 26.60 s,
faz) 78.12 A
R/S 32.80 Sy
42.30 Ag
(Rs) 37.22 Ss;
{R75} 59.68 A3
R/S. 2.00 Second Solution.
(R7s} 124.68 Area,
26.60 S,
[R/S] 17.28 A,
R/S. 32.80 S2
(R75) 42.30 Ay
(R7s] 11.30 S3
7S 120.42 As
t Statistics
Paired t Statistics
Given a set of paired observations from two normal populations
with means }4, u2 (unknown)
x Xe Xy
Yi v4 Yae-¥n
let
ww we
a ae Oe
ee
Section 10: Applications Programs V7
The test statistic
which has n ~ 1 degrees of freedom (df) can be used to test the null
hypothesis, Ho: 4) = up.
t Statistic for Two Means
Suppose (2), %2y ..- nj} and {¥1, ¥2) + ¥ng} are independent random
samples from two normal populations having means jy; and jg
(unknown) and the same unknown variance a
We want to test the null hypothesis Hp: y) — up =d.
Equations:
By
oo)
x= x;
ml
np
. ue
y= vi
ng ET
i~j-d
t= cane
1 7 i Bx? — ny x? + Ly? — nyy?
ny ng ny tny~2
We can use this t statistic (which has the t distribution with n, + ng
— 2 degrees of freedom (df)) to test the null hypothesis Ho.
References:
1. Statistics in Research, B. Ostle, lowa State University Press,
1963,
2. Statistical Theory and Methodology in Science and Engt-
neering, K.A. Brownlee, John Wiley and Sons, 1965.