IF A STUDENT SPENDS 15 HOURS PER WEEK STUDYING, IS THIS SIGNIFICANTLY DIFFERENT FROM THE POPULATION MEAN?

14 May IF A STUDENT SPENDS 15 HOURS PER WEEK STUDYING, IS THIS SIGNIFICANTLY DIFFERENT FROM THE POPULATION MEAN?

The Final Project is worth 105 points. Please download this document to your computer and save it as something easy to find like:Unit9FinalProjectYourName.

For this Project you will be using theProject Dataset in Doc Sharing under the Category called “Final Project Assignment and Data.” This dataset is in Excel and you will use Excel to complete this Project. You should enter your answers/responses/graphs/charts directly after the question.

After completing and saving the Project, submit your Project in the Drop Box. As you work on the Project, be sure to save often and also to email it to yourself. This will avoid project-loss.

The Math Center offers free tutoring and free project review.

Tutorials and Help can be found in Doc Sharing, the Live Binder, and YouTube Channel: ProfessorAmiGates (look for MM207 videos).

NOTE: This Project will require access to a z-table which can be found in Doc Sharing.

Name:

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?

Answer:

The relationship between GPA and SAT Score is stronger thank the relationship between GPA and AGE. Using Excel and the Correlation formula on excel, I was able to determine that GPA and AGE has an r-value or correlation coefficient of 0.233750588, while the GPA and SAT Score has an r-value of 0.320311, which is closer to 1, which also signifies a positive correlation. Both have a positive correlation, but GPA and SAT score is just greater.

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.

r-value is 0.377937-This makes this a positive correlation, for it’s a positive number and close to 1.

Kaplan MM207 Unit 9 Final Project Assignment 2016

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.

Project score = y

y = 0.2836(82) 54.474

y = 23.2552 54.474

y = 77.7292 or 78 so, the Project score is78.

2.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).

Mean: Add up all the values, and then divide by the number of values.

Project Score:

59 69 74 74 68 80 76 83 78 44 68 75 68 83 77 79 48 63 67 79 71 87 100 60 76 89 99 90 52 79 92 87 75 90 65=2548/34= 74.9 or mean=75

Final Exam Score:

75 89 78 90 89 87 94 81 45 89 85 87 96 97 89 53 83 45 54 51 62 70 42 52 59 73 75 35 65 80 69 66 74 46=2422/34=mean=71

Median: Arrange all data in order pick to middle as the median, if there are two middle values, add and divide by 2.

Project Score: 76 76=152/2= median is 76

Final Exam Score: 74 75=149/2=median is74.5

Mode:is the data that occurs more frequently in the dataset. It is possible that there is no mode in the dataset.

Project Score:68is the mode because it is the most repeated value.

59,69,74,74,68,80,76,83,78,44,68,75,68,83,77,79,48,63,67,79,71,87,100,60,76,89,99,90,52,79,92,87,75,90,65

Final Exam Score:89 is the mode because it is the most repeated value.

75 89 78 90 89 87 94 81 45 89 85 87 96 97 89 53 83 45 54 51 62 70 42 52 59 73 75 35 65 80 69 66 74 46

Range:is the difference between the lowest and the highest value, so Highest value – Lowest Value = Range.

Project score: 100-44=66is the range

Final Exam Score: 97-35=62is the range

Standard Deviation:is the square root of the variance.

Project Score: the square rootor the standard deviationof176.6954938 is13.29268572

Final Exam Score: the square root orthe Standard Deviation of313.8823529 is 17.71672523

Variance:Find the mean, then subtract the mean from each dataset, and square the difference. Add up all the squared values then divide by number of values minus 1 (because were looking for a sample variance) in the dataset.

Project Score: Variance is176.6954938

Final Exam Score: Variance is313.8823529

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.

The mean is the best measure of performance, for it is the average score of the data set. This shows that there aren’t much extremely low score. The mean shows me that the Project score has a higher average than the Final Exam Score.

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?

The Final Exam Score has the greater variation, for its variance is higher than the variance of the Project Score.

c) Who did better on the Final Exam, males or females?Justify your answerusing 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).

Male Female

mean

59.88235294

82.58823529

meadian

62

87

mode

0

89

Kaplan MM207 Unit 9 Final Project Assignment 2016This shows that Females did a lot better than the Males in the Final Exam, and the mean and median show that Female scores are higher on average, than the males. There are fewer males than 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 theirrelative 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 theMALE 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.