Mathematics

**USE THIS DATA SET: Data set.xlsx**

**1. ****Correlation, Scatterplots, and Prediction**

a. Which relationship is stronger, the relationship between GPA and AGE or the relationship between GPA and SAT score? Be sure to include all appropriate measures and explain and defend your answer. Is this result what you would expect, why or why not?

b. Create and paste in a scatterplot that compares Final Exam Score and Project Score. What is the correlation (r-value)? How would you describe the correlation (positive, negative, strong, weak, medium, none)? Include the “trendline” and “equation of the trendine” as part of your scatterplot.

c. Using the equation from your above scatterplot trendline, predict (estimate) the Project score for a person who gets a final exam score of 82. Show all of your work.

**Comparing and Describing Data**

For the Final Exam Score and then for the Project Score, calculate the mean, median, mode, range, standard deviation, and variance. (Hint: remember to use the sample std dev and sample variance).

a. Which two numerical measures offer you the best information for comparing performance between these two assignments? Use these two numerical measures to describe and compare student performance between the final exam and the Project.

b. Which variable, Final Exam Score or Project Score has greater variation of data? Which two numerical measures are best to offer this information? Choose the two numerical measures and use them to describe and compare the variation between the two variables. What does the variation tell you about student performance?

c. Who did better on the Final Exam, males or females? Justify your answer using at least THREE (3) numerical measures AND a bar graph. (Hint: Your bar graph will only show the mean and median values for the males and females).

**3. ****Relative and Absolute Differences**

a. Sally and Ron have decided to go back to school. Sally is 28 and Ron is 25. Based on their relative position, which of them (Sally or Ron) would be farther away from the average age of their gender group? Show all steps and work. (Hint: You will need to calculate z-scores as part of this question, which are the number of standard deviations from the mean).

b. Sally has a GPA of 3.35. What percentage of the students have a GPA above her GPA? Show all work. (Note: GPA is normally distributed).

c. SAT scores are normally distributed and can range from 0 to 1600. Ron’s SAT score is 800. What percentage of the MALE Student SAT scores in the dataset are below Ron’s SAT score? What would you say about Ron’s performance on the SAT test as compared to the other male students in the dataset? Show all work. (Hint: use z scores and the z table to solve this).

**4. ****Frequencies and Graphs**

a. A person’s GPA can be categorized into one of five classifications:

F: 0.00 – 0.49

D: 0.50 – 1.49

C: 1.50 – 2.49

B: 2.50 – 3.49

A: 3.50 – 4.00

Use these 5 categories and create a relative and cumulative frequency chart for all the GPAs in the dataset. You can do this by hand or you can use Excel.

b. Create a bar chart to show the frequencies of each letter grade.

**5. ****Confidence Intervals: The dataset for this Project represents a sample of data from a larger population. **

a. Use this dataset sample to calculate the 95% confidence interval for the true population mean time that all students spend studying per week. If a student spends 15 hours per week studying, is this significantly different from the population mean? Explain. Show all work and any use of Excel. You may choose to use Excel or you may do this by hand.

b. In your own words, explain why and how sample statistics are used to estimate population parameters. Using the dataset, create an example to support your explanation.

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