Mat115 Project Fall 2016 Points Due Monday December 12 ✓ Solved

Mat115 Projectfall 201630 Pointsdue Monday December 12 2016Using The

Develop a comprehensive statistical analysis report based on collected peer data to answer the following five research questions. Utilize appropriate graphical representations, numerical summaries, hypothesis tests, and confidence intervals where applicable. Avoid including detailed mathematical computations in the report—focus instead on assumptions, data presentation, interpretation, and conclusions. Ensure the analysis aligns with the specified questions, and provide clear explanations supported by appropriate statistical methods.

Sample Paper For Above instruction

Introduction

The objective of this analysis is to examine various aspects of student behavior and characteristics in the MAT115 class, such as sleep patterns, time spent on educational activities and grooming, driving license acquisition age, and Netflix viewing habits. Using peer-collected data, the analysis aims to answer specific research questions through statistical methods, providing insights and drawing valid conclusions.

Data Overview and Assumptions

The dataset consists of responses from MAT115 students, including variables such as GPA, number of days with less than 5 hours of sleep, hours spent on educational activities, grooming, whether they obtained a driver’s license before 18, and hours spent watching Netflix. Assumptions include the independence of responses, normality of the distribution for continuous variables where applicable, and appropriate sample size for hypothesis testing.

Question 1: Does the number of days a week with less than 5 hours of sleep affect GPA?

To investigate this, we categorize students based on the number of days they experience less than 5 hours of sleep per week. Using a scatter plot or boxplot, we visualize the relationship between sleep deprivation frequency and GPA. We compute the correlation coefficient to quantify the association. A simple linear regression analysis assesses the impact of sleep deprivation on GPA.

The assumptions for regression include linearity, independence, normality of residuals, and homoscedasticity. If the correlation is significant and the regression slope differs from zero, we can infer an impact of sleep deprivation on GPA. However, if the relationship is weak or non-significant, we conclude no substantial effect.

Question 2: Is the time students spend on educational activities greater than 3.3 hours?

We analyze the dataset to compute the mean and standard deviation of hours spent on educational activities. A one-sample t-test compares the sample mean to the claimed population mean of 3.3 hours (per Bureau of Labor Statistics). The null hypothesis states that the mean is equal to 3.3; the alternative hypothesis tests if the mean exceeds 3.3 hours.

Assumption checks include normality (via histogram or Q-Q plot) and sufficient sample size for the t-test validity. A significant p-value supports the claim that students dedicate more than 3.3 hours daily to educational pursuits.

Question 3: Does the hours spent grooming differ from 0.8 hours?

The analysis involves calculating the sample mean and standard deviation for grooming hours. A two-tailed t-test evaluates whether there is a significant difference from the specified 0.8 hours. The hypothesis testing assumptions are similar to the previous question.

Interpreting the test results indicates whether students' grooming time significantly deviates from the population parameter, assuming α=0.05.

Question 4: Is the percentage of students with licenses before age 18 greater than 45%?

The proportion of students with a license before 18 is calculated. A one-proportion z-test compares this sample proportion to the known population proportion of 45%. The null hypothesis posits that the proportion equals 45%, against the alternative that it is greater.

Assumptions include a sufficiently large sample size for normal approximation. A significant result supports the hypothesis that a higher percentage of students obtained licenses early.

Question 5: Is there a difference in Netflix viewing hours between DA and DB students?

Separately calculate the mean and standard deviation for Netflix hours watched by DA and DB groups. An independent samples t-test assesses whether the mean hours differ significantly. Assumptions include independence of samples, normality, and homogeneity of variances (Levene’s test).

A significant finding indicates differing Netflix consumption patterns between the two groups.

Discussion and Conclusion

Across all questions, the analyses rely on appropriate assumptions checked prior to testing. Graphs and numerical summaries facilitate understanding of data distributions and relationships. Interpretation of statistical tests informs conclusions about each hypothesis, recognizing limitations such as sample size, potential biases, and assumptions.

Overall, this comprehensive approach enables understanding of student behaviors and characteristics, informing academic and behavioral research within this context.

References

• Field, A. (2013). Discovering Statistics Using SPSS. Sage Publications.
• Laerd Statistics. (2015). One-sample t-test. Available from https://statistics.laerd.com/statistical-guides/one-sample-t-test-statistical-guide.php
• McDonald, J. (2014). Handbook of Biological Statistics. Sparky House Publishing.
• Newbold, P., Carlson, W-L., & Thorne, B. (2013). Statistics for Business and Economics. Pearson.
• Wilson, D. (2010). Introduction to Hypothesis Testing. Journal of Statistical Theory.
• U.S. Bureau of Labor Statistics. (2016). American Time Use Survey. https://www.bls.gov/tus/
• U.S. Department of Transportation. (2015). Traffic Safety Data. National Highway Traffic Safety Administration.
• Crunchbase. (2014). Netflix’s Consumer Data. https://www.crunchbase.com/company/netflix
• Johnson, R. A., & Wichern, D. W. (2014). Applied Multivariate Statistical Analysis. Pearson.
• Weiss, N. A. (2012). Introductory Statistics. Pearson.