Single sample t statistic

Psychology 201 Prof. Rick Zinbarg

The meaning of the t-test: A comparison of 2 studies Which one more likely to reject the null hypothesis? (answer without actually computing the t values)

Study 1 Study 2Subject Inteliagra Cortexin1 123 1222 122 1223 110 1104 110 1105 109 1096 109 1097 107 1078 106 1069 106 10610 106 10611 95 9512 95 9513 94 9414 94 9415 93 94M 105.27 105.27

H0 :X = 100H1 :X 100

Ch. 12, Problem 9(p. 260)

1.

2.

H0 : = 5.3H1 : 5.3

Relative

Frequency

0 t

2

2

= .05,2 = .025df = n 1 = 10 1 = 9

t(.025) =

Ch. 12, Problem 9(p. 260)

1.

2.

H0 : = 5.3H1 : 5.3

Relative

Frequency

0 t

2

2

RR: Reject Ho if t(obs) or t(obs)

t(.025) =

= .05,2 = .025df = n 1 = 10 1 = 9

X=# of cigarettes smoked per day after new program

X X204

016

31

91

62

364

52

254

21

41

= 26 100

M = Xn=2610 =

s =X2 ( X)

2n

n 1

=100 (26)

2

109

= 1.897

sM =sn

=1.89710

=

t(obs ) =M 0sM

, sM =sn

3.

4. < -2.262 , therefore reject Ho.

The new therapy is effective at helping people reduce their smoking than the standard therapy

t(obs) =2.6 5.3.5999 =

Using single sample t statistic to construct confidence intervals Use data from Ch. 12, #9 to construct a 95% CI for the of the # of cigarettes smoked per day after new program

(1 )%CI for = M t(2 )sM

#

$%

&

'(

1 = .95 = .052 =df = n1=101=

.475

.475

.025

.025

Mobs2.6

t(.025)

-t(.025)

t(.025) = 2.262

(1 )%CI for = 2.6 2.262 *.5999[ ]95%CI =