Assignment:
Many college instructors believe that students need to spend at least 2 hours studying outside of class for every hour of lecture. They believe that the number of hours students study to prepare for the exam affect students' marks significantly. As opposed, some believe that the number of preparation hours do not essentially affect students' marks while some other factors are to be considered.
To study the relationship between the preparation time spent by each student (in hours) for the exam and the reported mark, a sample of 100 students were selected randomly from a large statistics class.
Using EXCEL, answer below 9 questions:
1. What type of survey method is used and why?
2. What sampling method could be used to select the sample and why?
3. What are the variables we should consider collecting data for the purpose of the analysis and why? Identify the data type(s) for the variables.
4. What kind of issues we may face in this data collection?
5. Using 8 classes and intervals of 20 - 30, 30 - 40, etc for the preparation time and 8 classes and intervals of 20 - 30, 30 - 40, etc for marks, develop a distribution table including class intervals, frequency, relative frequency and cumulative relative frequency for each variable. Then, draw frequency histogram, relative frequency histogram and cumulative relative frequency histogram for each variable. Comment on the shape of frequency histogram for each variable.
6. Use an appropriate plot to investigate the relationship between the two variables. Briefly explain the selection of each variable on the X and Y axes and the reason? Draw the fitting line for the plotted observations.
7. Present the equation of the estimated fitting line (regression) in your answer to Question
6. Estimate the effect of an increase in preparation time by one hour on students' mark and interpret it.
8. Prepare a numerical summary report about the data on the two variables by including the summary measures, mean, median, range, variance, standard deviation, smallest and largest values, three quartiles, interquartile and the 30th percentile for each variable.
9. Compute a numerical summary measure to measure the strength of the linear relationship between the two variables. Interpret this value.