Question

When people learn a new task, their performance usually improves when they are tested the next day, but only if they get 6 hours sleep (Sticckgold, et al., 2000). The following data demonstrate this phenomenon. The participants learned a visual discrimination task on one day. Half of the participants were allowed to have at least 6 hours of sleep and the other half were kept awake all night. 6 hours sleep No sleep n =14 n = 14 M = 72 M =65 SS = 932 SS = 706 Is there a significant difference between the two conditions? Use a two-tailed test with LaTeX: \alphaα = .01.

Answer 1

Answer:

consider,

degree of freedom = n1+n2-2

= 14 + 14 - 2

= 26

Here alpha = 0.01,df = 26

critical t value = +/- 2.78

Pooled variance = S^2p = (SS1 + SS2)/(df1+df2)

substitute values

= (932 + 706)/(13+13)

= 63

Now consider,

test statistic = (x1-x2)/sqrt(s^2p(1/n1 + 1/n2))

substitute values

= (72 - 65)/sqrt(63(1/14 + 1/14))

= 7/3

= 2.33

Here we observe that, test statistic < critical value, so we fail to reject Ho. So there is no sufficient evidence.