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I need help with this problem. I already know the answer. I am confused between the lectures, textbook, and work text. Can you show me, the old fashioned way (not Excel, SPSS or any other software to generate the answer), I need the formulas to show how to come up with the correct answer?

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An experiment was performed to measure the effect of sleep deprivation on cognitive performance. twenty college juniors were randomly selected from a group of volunteers and arbitrarily assigned either to a sleep deprivation group or to a control group. The participants in the sleep deprivation group were kept awake for 24 hours; the members of the control group had a normal night's sleep. Participants were then asked to perform a simple mental arithmetic task, and the time it took each participant to complete the task was recorded. The results were as follows:

Sleep Deprivation Group
(Time in seconds)
10
15
13
5
27
7
16
20
21
13

Control Group
(No sleep deprivation)
(Time in seconds)
13
8
14
11
8
7
2
2
17
5

Determine whether or not the groups differ significantly. if you reject the null hypothesis, tell what it means in the context o the problem. Give the table values for significance.

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