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# A study was conducted to determine the effects of sleep deprivation on student's ability to solve problems.

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A study was conducted to determine the effects of sleep deprivation on student's ability to solve problems. The amount of sleep deprivation varied over 8, 12, 16, 20, and 24 hours without sleep. A total of ten subjects participated in the study, two at each deprivation levels. After a specified sleep deprivation period, each subject was administered a set of simple addition problems, and the number of errors was recorded. The following results were obtained:
Number of Errors (y) Number of Hours Without Sleep
8 8
6 8
6 12
10 12
8 16
14 16
14 20
12 20
16 24
12 24
1. Find the least squares regression model
2. Calculate and interpret the result
3. Does the data present sufficient evidence to conclude that there is a relationship between the number of errors and the number of hours without sleep?
4. Find the observed significance level for the test and interpret its value
5. Find the coefficient of determination and interpret its value
6. Find the coefficient of correlation and interpret its value
7. Find the significance level for the regression model and interpret its value.
8. Determine the 95% confidence interval and interpret its value

#### Solution Summary

A study was conducted to determine the effects of sleep deprivation on student's ability to solve problems. The amount of sleep deprivation varied over 8, 12, 16, 20, and 24 hours without sleep. A total of ten subjects participated in the study, two at each deprivation levels. After a specified sleep deprivation period, each subject was administered a set of simple addition problems, and the number of errors was recorded. The following results were obtained:

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