Statistics Project – Directions: Ask yourself a question regarding the mean of a certain characteristic of a population:
- I believe the average family owns 2.5 pets.
- I believe the average person watches 10 hours of TV per week.
- I believe the average NFL player plays 15 games per season.
- I believe the average egg weighs 25 ounces.
Collect between 60 and 100 numerical data values. These data values will be the sample in your study.
You can collect these values using one of the two methods described below:
(a) Use sources such as the internet, newspapers, encyclopedias, etc. to take a sample of at least 60 data values.
(b) Create a survey question on a topic of your choice and give the survey to at least 60 people.
Your survey should consist of only one question. Make sure that the answers that people will give you will be numbers, not words, labels, “yes” or “no”, etc.
Be aware what the population for your sample is (all US families, all residents of my city, all NFL players, all eggs, etc.). The population should be significantly larger than your sample.
With the collected data, do the following:
Create a title page with your name, the course and section, the semester, and a meaningful and descriptive title for your project. From reading your title page, it should be clear what your project is about.
Part I: StatCrunch Work
Enter the data values you collected into a column in StatCrunch and do each of the following:
(a) Compute the basic descriptive statistics for your sample, including the number of data, mean, median, mode, variance, standard deviation, minimum, maximum, range, first quartile, and third quartile.
(b) Make a frequency histogram and a boxplot for your data. Each graph should have a meaningful title and labels on the axes, describing what the graph is and what the data values are.
(c) Compute a 95% confidence interval for the population mean.
Part II: Writing Component
Use the information obtained above to thoroughly answer each of the following questions.
(a) Give a thorough description of what you are studying in your project, and what your assumption for the mean is.
(b) Explain what the population and sample are in your study. Explain how you collected the sample values in detail. Make sure to cite any sources that you used. If you gave a survey, clearly describe how and where the survey was administered.
(c) Is the sample you selected a random sample? Why or why not? Do you think that the sample you selected accurately represents the population you are studying, or do you think there may be some sources of bias?
(d) Does your frequency histogram seem to be close to any of the following shapes: bell-shaped, uniform, bimodal, skewed left, or skewed right? Or does it resemble a combination of them or none of them at all? Explain your answer.
(e) Using the answers StatCrunch gave you for the sample mean 𝒙̅ and the sample standard deviation 𝒔, determine what percentage of the values in your sample lie within 1 standard deviation, 2 standard deviations, and 3 standard deviations of the mean. Show your work!
(f) State the empirical rule and compare it to the percentages you found in part (e). Are the values close or is there a big difference? Considering this and the shape of your histogram from part (d), answer whether your data appears to be normally distributed or not.
(g) Using the confidence interval obtained in part 1(c), answer whether your guess for the mean might be correct or not.
• The entire project must be typed and submitted in pdf format.
• All writing components of the project should be answered using paragraphs, complete sentences, and grammatically correct English. The detail and quality of your writing will be part of your grade as well. You will be graded not only on statistical correctness and detail, but also on neatness, presentation style, and creativity.
• The writing component of your project should be at least two full pages, double spaced, with size 12 font. However, this is the minimum, and more may be necessary to receive a higher grade on this part of the project.
At a Glance
Page 1: A title page with all the information requested above
Page 2: A list of all your sample values (from StatCrunch or otherwise)
I. StatCrunch Work:
Page 3: Print out the Descriptive Statistics requested in I(a)
Page 4: Frequency Histogram with meaningful title and labels
Page 5: Boxplot with meaningful title and label
Page 6: Print out the Confidence Interval requested in I(c)
(if it is possible to fit these on fewer pages, that is fine)
II. Writing Component:
Pages 6 and 7 (or more): Thorough answers to questions II(a) – (g).
The following grades will be given:
50% Content of Writing Part II
30% Content of Minitab Part I
20% Quality of the title page, overall presentation, neatness, and creativity All work submitted must be your own work. Submitting work that was done by another student or any other individual is plagiarism and cheating. Any student caught cheating on any part of this project will receive an overall grade of 0 on the entire project, even if cheating only occurred on one part of the project.