Question

1. In a study examining the power of imagination, Cervone (1989) asked subjects to think about factors that could influence performance on solving maze-like puzzles. In one condition, participants imagined positive factors that could make the task easier, and in another condition, participants imagined negative factors that would make the task more difficult Later Cervone measured task persistence: how long the participants continued working on task (or how quickly person gave up).

Positive condition:           n = 12                    M = 28                  SS = 280

Negative condtion:         n = 12                    M = 22                  SS = 248

Do the data support the conclusion that imagination can have a significant effect on task persistence? Use α = .05. Also, compute estimated d and r² for the test.

Answer 1

For Positive Condition :   

x̅1 = 28, n1 = 12

SS = 280

s1 = sqrt(SS/(n-1)) = 5.0452

For Negative Condition :   

x̅2 = 22, n2 =12

SS = 248

s2 = sqrt(248/11) = 4.7482

α =    0.05
  
Null and Alternative hypothesis:  

Ho : µ1 = µ2  

H1 : µ1 ≠ µ2  

Pooled variance :  

S²p = ((n1-1)*s1² + (n2-1)*s2² )/(n1+n2-2)

= ((12-1)*5.0452² + (12-1)*4.7482²) / (12+12-2) = 24.0000

Test statistic:  

t = (x̅1 - x̅2) / √(s²p(1/n1 + 1/n2 ) = (28 - 22) / √(24*(1/12 + 1/12)) =    3.0000

df = n1+n2-2 =    22

Two tailed p-value = T.DIST.2T(ABS(3), 22) =    0.0066

Decision:  

p-value < α, Reject the null hypothesis  

Conclusion:  

There is enough evidence to conclude that imagination have a significant effect on task persistence.

Cohen's d = (x̅1- x̅2)/√s²p =    1.2247

r² = t²/(t²+df) = 3²/(3²+22) =    0.2903