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 = 706Is there a significant difference between the two conditions? Use a two-tailed test with � = .01.Remember use the attached t-distribution chart when obtaining your critical region. ### The Impact of Sleep on Learning New TasksResearch shows that learning a new task is significantly impacted by sleep. Performance tends to improve if individuals receive at least 6 hours of sleep before being tested the next day. This effect is supported by the research data from Stickgold et al. (2000).In a study, participants learned a visual discrimination task. They were divided into two groups:- **6 Hours Sleep Group** - Number of participants (n): 14 - Mean performance score (M): 72 - Sum of squares (SS): 932 - **No Sleep Group** - Number of participants (n): 14 - Mean performance score (M): 65 - Sum of squares (SS): 706**Research Question**Is there a significant difference in task performance between those who slept for 6 hours and those who did not sleep? A two-tailed test with a significance level (\(\alpha\)) of 0.01 is used to determine this.**Reminder**Use the provided t-distribution chart to find the critical region for the test.

Given that : 6 hours sleepNo sleepn =14n = 14M = 72M = 65SS = 932SS = 706Claim : 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. Let µ1 be the population mean of people sleeping for 6 hours Let µ2 be the population mean of people with no sleepThe test of hypothesis is given by : The t - statistic is given by : Substituiting the values in the t - statistic formula we get : It is two - tailed test with α = .01 Looking into the two - tailed combined table with degree of freedom ( n -1 ) = 13 and α = 0.01; where n = 14 ( given ) The t - critical value = 3.012Note : For two tailed test α = 0.01 is equally distributed on both side of the tail i.e left side and right side.With α/2 = 0.05 on the left side and α/2 = 0.05 on the right sideThe critical value is given for two - tail combined i.e. α/2 + α/2 = 0.01 DECISION RULE When t - statistic < t - critical value. Do Reject Ho. When t - statistic > t - critical value. Reject Hot - statistic ( 2.33) < t - critical value ( 3.012)We fail to Reject Ho and conclude that there is no sufficient evidence that when people learn new task performance improves only if they get 6 hours sleep.We fail to reject Ho and conclude that there is no sufficient evidence that when people learn new task performance improves only if they get 6 hours sleep.