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DMI - Assignment Example

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A number of researchers have hypothesized that a relationship exists between the number of hours of sleep and exam performance. Other factors that have been known to affect performance…
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Download file to see previous pages Data was collected on the following variables:
For the variable on the time of study, the histogram shows that 61% of respondents studied at night while the remaining 39% studied during the day. Studying until late in the night can have an impact on the results as a student takes exam while the brain is fatigued and is not functioning at its optimum.
The histogram and summary statistics for number of hours slept is shown above. From the results, we see that the average hours of sleep for grade 12 students are 6.5 hours with a standard deviation of 1.35. It has been recommended that students should sleep for at least 6 hours to maximize their cognitive ability.
A scatterplot of age versus hours slept shows a negative correlation, i.e. older persons tend to sleep fewer hours as compared to younger ones. Indeed, the results from the scatterplot are further confirmed by results from the correlation table. The correlation is -0.725 implying a negative correlation between the two variables.
A plot of exam score against hours slept shows a positive correlation between the two variables. Further analysis through correlation shows a value of 0.617. Consequently, the preliminary analysis supports the null hypothesis that academic performance is positively related with the number of sleep hours. Further analysis through regression is needed to build confidence in this hypothesis.
Final analysis of the data involved regression modeling using exam scores as the dependent variable and hours slept, age and food quality as the independent variables. The regression equation can be stated as follows:
From the equation, it is observed that the intercept for the number of hours slept is positive implying that hours of sleep positively impacts test scores. This can be stated as follows: a unit increase in hours slept results into a 4.479 unit increase in examination scores. However, age and food quality have a ...Download file to see next pagesRead More
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