Page 267 - DMGT404 RESEARCH_METHODOLOGY

Unit 12: Hypothesis Testing

Notes
-
x y
t =
æ 1 1 ö
s 2 ç è n 1 + n 2 ø ÷
Here n = 5 n = 7
1 2
x = 230, y = 399

2

 ( x x- ) = 310 , ( y - ) y 2 = 399
 x 230
x = n = 5 = 46
1
 y 399
y = = = 57
n 2 7

1 2 ) }
2
s = ( {å x - ) x + å ( y - y
2
n + n - 2
1 2
D.F. = (n + n – 2) = (5 + 7 – 2) = 10
1 2
1
s = {310 674+ } 98.4=
2
10
-
46 57
t =
æ 1 1ö
98.4 ´ ç + ÷
è 5 7 ø
- 11
= æ 12 ö
98.4 ´ ç ÷
è 35 ø
- 11 11
= = -
33.73 5.8
= – 1.89
t at 10 d.f. at 5% level is 1.81.
Since, calculated t is greater than 1.81, it is significant. Hence H is accepted. Therefore the two
A
nutrition programmes differ significantly with respect to weight increase.

Two Tailed t-Test

When two samples are related we use paired t-test for judging the significance of the mean of
difference of the two related samples. It can also be used for judging the significance of the
coefficients of simple and partial correlations.
The t-test is performed using the following formula;
n - 2
t = r
yx -
1 r yx

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