Week to Week Group Assignments for ST370

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School

North Carolina State University *

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Course

370

Subject

Statistics

Date

Feb 20, 2024

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docx

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Uploaded by loganprillaman

Week to Week Group Assignments for ST370 1) Week 1 (January 8 – 12) – Create groups and capture group information in a shared spreadsheet. – Complete – All groups earned 5 points 2) Week 2 (January 16 – 19) All group members complete fill out columns in spreadsheet for each variable specified. All groups earn 5 points provided each member provides information. One point deduction for each member who does not comply. – Due Friday 1/19 at midnight. 3) Week 3 (January 22 – 26) Each group selects one qualitative and one quantitative variable from the spreadsheet that they wish to study. The group captures this information in column A (which is currently empty). For instance if the group selects number siblings and hair color (columns G and K) then they should enter G, K in column A, using any of the rows corresponding to their group. a. We will use STATCRUNCH for the analysis. Begin by selecting a random sample of size 30, for the quantitative variable you have chosen. To do this download the class spreadsheet to your laptop and then open STATCRUNCH by clicking on the link in the left side bar in Moodle. b. To bring your data into STATCRUNCH on the top bar select “DATA” and then “Load” and follow the instructions. i. We want to start with a sample of size 30; to do this simply select “DATA” and “SAMPLE”. ii. Compute summary statistics, consisting of the mean, median mode, quartiles and standard deviation. Do this by selecting “STAT”, “SUMMARY STAT” and then “COLUMN” as your data is in columns. Continue by selecting the statistics you wish to compute. Hold down the CTRL key to select multiple statistics. Enter that information on the sheet for your group. Discuss the relationship of the mean to the median. Do you believe the data is right skewed, left skewed or symmetric based on the relationship of the mean to the median. Given the variable you have chosen does it seem reasonable that this would be the case? iii. Construct a boxplot and histogram. Use the “GRAPH” option. Is the skew consistent with your answer in part b? iv. Comment on whether you observe any outliers. Do you believe they should be investigated? For instance is the value completely unreasonable and needs to perhaps be corrected. v. Based on your analysis above is the mean or the median a better measure of center? vi. Which quartile is most compact? Which quartile has the most variability? vii. For the qualitative variable you have selected: 1. Construct a bar chart. Select “Graph” “bar plot” “with data”. Is there some data cleanup that might need to be done. Explain.

2. Identify the modal category. (this may require you perform some data cleanup before doing so). c. Write up a 3 – 4 sentence summary of each variable so that a reader has a good idea of the dataset based on the information you obtained above. 4) Week 4 (January 29 – Feb 2) We will complete two short exercises this week using the variables we selected last week. The first task is on conditional probability and the second gives you an opportunity to use your sample results for your quantitative variable by comparing it to the results obtained by analyzing the entire population. a. Use the template for week 4 found in our group project folder on Moodle to enter your responses to the analysis below. Have one person in your group upload the work to Gradescope. b. Task 1 - Conditional Probability – Create a conditional probability question using the qualitative variable as the given or conditioning variable. For instance suppose you selected family car color for the qualitative variable and miles from campus for the quantative variable. A possible conditional probability question could be, “ given that the family car color is white what is the likelihood a randomly selected student lives 50 miles or less from campus” Let A be the event the person lives 50 miles or less from campus. Let B be the event the family car color is white. Then we need to find P(A|B). Recall the formula; P(A|B) = P(A and B)/P(B). i. For the numerator: Using your sample, find all pairs where car color is white and miles from campus is ≤ 50 miles. This is the size of the event. Divide by the sample size (30) to get P(A and B). ii. For the denominator: Count all the white cars in your sample. Divide by 30 to get P(B). iii. Divide P(A and B) by P(B) to get P(A|B). iv. Did you compute empirical probabilities above, or do you compute theoretical probabilities? v. Are the events A and B independent or dependent? You must provide details. A simple yes or no is NOT sufficient. vi. When reporting out your result you must show some work for each step. c. Task 2 – Comparing the quantitative variable from the sample to the same variable across the entire population. i. Using your quantitative variable of interest and the ENTIRE master spreadsheet, which represents the population, find: 1. The population mean 2. The population median 3. Create a graph of the population distribution. ii. Compare these values to the values you obtained for the sample mean and median from week 3. Are they similar or quite different?

iii. Compare the sample distribution from week 3 with the population distribution. 1. Which one has more variability? 2. Do either have outliers? 3. Are they similar in shape?

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