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 α = .01.Remember use the attached t-distribution chart when obtaining your critical region. # Table B.2: The t Distribution## OverviewThis table provides the values of t corresponding to proportions in one tail or in two tails combined. It is commonly used in statistical analyses involving t-tests.### Illustrations- **One Tail**: This diagram represents the area under the curve in one tail (either right or left) of the t distribution.- **Two Tails**: This diagram represents the area under the curve in both tails combined of the t distribution.### Table DescriptionThe table lists the values of t for different degrees of freedom (df) and for various proportions. The columns display values corresponding to different proportions in one tail and two tails combined.#### Proportions in One Tail- 0.25- 0.10- 0.05- 0.025- 0.01- 0.005#### Proportions in Two Tails Combined- 0.50- 0.20- 0.10- 0.05- 0.02- 0.01### Table Data| df | 0.50 | 0.25 | 0.20 | 0.10 | 0.05 | 0.025 | 0.01 | 0.005 ||-----|------|-------|-------|-------|-------|-------|-------|-------|| 1 | 1.000| 3.078 | 6.314 | 12.706| 31.821| 63.657| | || 2 | 0.816| 1.886 | 2.920 | 4.303 | 6.965 | 9.925 | | || 3 | 0.765| 1.638 | 2.353 | 3.182 | 4.541 | 5.841 | | || 4 | 0.741| 1.533 | 2.132 | 2.776 | 3.747 | 4.604 | | || 5 | 0.727| 1.476 | 2.015 | 2.571 | 3.365 | 4.032 | 4.604 | ||

Name: When people learn a new task, their performance usually improves when
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: 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 disc

Given that : 6 hours sleep No sleep n =14 n = 14 M = 72 M = 65 SS = 932 SS = 706 Claim : 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 sleep The 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 = 3.012 Note : 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 side The 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 Ho t - 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.