Analysis of Statistical Concepts in Sleep Deprivation Study

In a recent study on the effects of sleep deprivation on cognitive performance, researchers recruited 100 college students. They assigned half of the participants to a sleep-deprivation condition where they were only allowed to sleep for 4 hours, and the other half were assigned to a control group that could sleep for 8 hours. After one week, both groups completed a series of cognitive tasks measuring memory, attention, and problem-solving skills. The researchers reported that participants in the sleep-deprivation group had significantly lower scores on all cognitive tasks compared to the control group.

Using the scenario above, analyze the statistical concepts that are relevant to evaluate the findings of this study. Discuss the importance of the independent and dependent variables, types of statistical tests that could be used to analyze the data, potential confounding variables, and the implications of the results regarding generalizability to a broader population.