Statistics Exam 2

Stat 100 Exam 2 Review Notes

Overview of Exam Content

• This review provides an idea of the types of questions that may be on Exam 2.

• It does not indicate exact questions or topics.

• Exam 2 covers material from Textbook Chapters 4 and 7.

• Recommended to review class notes, activities, homework, and the textbook for extensive practice.

• A variable types chart will be provided during the exam, make sure to practice using it.

Dataset Overview

• The dataset used in hypothetical questions pertains to NFL football players from the 2025 season, comprising the following 10 columns:

  • Player Name

  • Position (e.g., Quarterback, Running Back)

  • Jersey Number

  • Height (in inches)

  • Weight (in pounds)

  • Age (in years)

  • Number of seasons in the NFL

  • Draft Round Selection (1st, 2nd, …)

  • Number of touchdowns scored last season

  • Performance rating (scale of 1-10 assigned by coaches)

Questions 1-6

1. Visualization of Number of Seasons in the NFL:

   • Appropriate graphics to visualize the variable:

     • a. Bar plot

     • b. Histogram

     • c. Side-by-side Boxplot

     • d. Scatterplot

2. Summarizing Draft Round Selection:

   • Appropriate statistic to summarize:

     • a. Mean

     • b. Proportion

     • c. Difference in Means

     • d. Difference in Proportions

3. Symbol for Draft Round Selection Summary:

   • Appropriate symbol:

     • a. $\bar{x}$

     • b. $ext{µ}$

     • c. $ext{p̂}$

     • d. $p$

4. Point Estimate for Average Weight by Position:

   • Appropriate point estimate:

     • a. Sample proportion

     • b. Difference in population means

     • c. Population Mean

     • d. Difference in sample means

5. Shape of Distribution based on Five-Number Summary:

   • Given five-number summary for touchdowns:

     • min: 0, Q1: 1, median: 1, Q3: 2, max: 7

   • Choose all applicable descriptions:

     • a. Skewed right

     • b. Skewed left

     • c. Symmetric

     • d. Cannot tell symmetry/skew from this information

     • e. Unimodal

     • f. Bimodal

     • g. Cannot tell modality from this information

6. Players Scoring 2 to 7 Touchdowns:

   • Options for number of players who scored within this range:

     • a. 25 players

     • b. 59 to 60 players

     • c. 75 players

     • d. 119 players

Questions 7-10

• Website Development Teams Study: Analysis on the number of websites completed and delivered per quarter by 3-person teams from January 2001 through August 2002.

1. Distribution of Websites Delivered in 2002:

   • Shape description options:

     • a. Unimodal symmetric

     • b. Unimodal left-skewed

     • c. Bimodal symmetric

     • d. Linear

   • Statistics to describe center and spread options:

     • i. Mean and Range

     • ii. Median and IQR

     • iii. Mean and Standard deviation

     • iv. Median and Standard deviation

2. Mean vs. Median Relation in 2002 Distribution:

   • Expectation on mean relative to median:

     • a. Mean approximately equivalent to median

     • b. Mean greater than median

     • c. Mean less than median

     • d. Cannot approximate mean relative to median

3. Standard Deviation Comparison:

   • Options:

     • a. Larger in 2001

     • b. Larger in 2002

4. Labeling Statements for Histogram and Barplot:

   • Statement Checkbox:

     • a. Width of the bars is meaningless.

     • b. The y-axis measures the frequency of cases within each bar.

     • c. Bars may be reordered.

Questions 11-21

• GPA Exploration Study: Analysis of GPAs from 120 randomly selected freshmen at a small college.

1. Population of Interest:

   • Options include:

     • a. All college students

     • b. All students from this college

     • c. All freshmen

     • d. 120 freshmen

     • e. 120 students

2. Population for Generalization:

   • Potential options for generalization include:

     • a. All freshmen

     • b. All freshmen from this college

     • c. All students from this college

     • d. 120 college students

     • e. 120 freshmen from this college

3. Variable Type for GPA:

   • Options:

     • a. Numeric continuous

     • b. Numeric discrete

     • c. Categorical ordinal

     • d. Categorical nominal

4. Distribution Shape:

   • Options for describing shape:

     • a. Unimodal symmetric

     • b. Unimodal left-skewed

     • c. Unimodal right skewed

     • d. Symmetric, but can’t determine modality

     • e. Left-skewed, but can’t determine modality

     • f. Right-skewed, but can’t determine modality

5. Justification for Shape Answer:

   • Evidence to support shape selection must be provided.

6. False Statement About Boxplots:

   • Options:

     • a. Box displays the middle 50% cases.

     • b. Easily identifiable outliers.

     • c. Change bin width of the box.

     • d. Built from robust statistics.

7. Students with GPAs between 2.7 and 3.6:

   • Options:

     • a. 30

     • b. 50

     • c. 60

     • d. Cannot determine with the information given.

8. True Statement Options:

   • Options:

     • a. More students with GPA > 3 than < 3.

     • b. Lower fence at 1.5.

     • c. More students < 2.7 than > 3.6.

     • d. Lower 25% of GPAs have more variability than upper 75%.

9. Estimating Population Mean GPA:

   • Best estimate:

     • a. Point estimate $\bar{x}$

     • b. Deviation $\bar{x}$

     • c. Study $ext{µ}$

     • d. Parameter $ext{µ}$

10. Calculating Dataset Standard Deviation:

    • Statements about standard deviation:

      • a. Value greater than 0.

      • b. Measures distance from each point to the median.

      • c. Negative number due to left skew.

      • d. Unitless statistic.

11. Appropriate Measure of Center:

    • Determine mean or median as better measure of center.

    • Explanation required using 4-sentence structure for statistical reasoning.

Questions 22-32

• Predicting GPA from ACT Scores Study: Analysis created to determine if GPA can be predicted from ACT scores using the same sample.

1. Linear Relationship Description:

   • Describe the relationship between ACT score and GPA.

2. Correlation of ACT Score and GPA:

   • Possible correlation values:

     • a. 0.005

     • b. 0.073

     • c. 0.269

     • d. 0.431

3. Regression Line Equation:

   • Write the equation of the linear regression line.

4. Intercept Interpretation:

   • Explain intercept in the context of the study.

5. Slope Interpretation:

   • Explain slope in the context of the study.

6. R^2 Value Interpretation:

   • Explain the significance of R^2 value in this context.

7. Expected GPA Calculation:

   • Calculation for expected GPA for an ACT score of 22 and show work.

8. Residual Calculation:

   • Calculate and interpret the residual for a student earning a 22 on ACT and 2.54 GPA.

9. Predicting GPA for ACT Score of 10:

   • Determine if predicting is appropriate and explain.

     • a. Yes to predict

     • b. Score range use

     • c. No, outside data range

     • d. No, other variables might explain

10. True Statement About Variables:

    • Options:

      • a. Swapping variables gives the same equation.

      • b. Correlation gives form, strength, direction of relationship.

      • c. Correlation values of -0.87 and 0.87 have same strength.

      • d. We could compare with boxplots instead.

      • e. High correlation indicates causation.

11. ACT Score Needed for GPA ≥ 3.0:

    • Determine necessary ACT score for a GPA of 3.0.

    • Explanation using 4-sentence structure required for reasoning.

Questions 33-45

• Nicotine Lozenge Effectiveness Study: Randomized assignment of smokers to nicotine or placebo lozenge to monitor abstinence success over a year.

1. Contingency Table Values:

   • Fill values for Success and Not Successful groups in the table.

2. Type of Study:

   • Classify as observational study, experiment, or randomized experiment.

   • Justify classification.

3. Best Graphic Representation Choice:

   • Options:

     • a. Histogram

     • b. Side-by-side barplot

     • c. Side-by-side histogram

     • d. Barplot

4. Proportion Calculation for Nicotine Lozenges Not Successful:

   • Show calculations for proportion.

5. Proportion for Nicotine Lozenges Among Not Successful Smokers:

   • Show calculations for proportion.

6. Proportion of Smokers Successfully Abstaining with Nicotine Lozenges:

   • Show calculations for proportion.

7. Proportion of Smokers Abstaining with Placebo Lozenges:

   • Show calculations for proportion.

8. Proportion Successful with Placebo:

   • Show calculations for proportion.

9. Explanatory and Response Variables:

   • Determine for the study.

   • Response: Abstinence success

   • Explanatory: Lozenge Type

10. Calculate Point Estimate for Proportions:

    • Calculate and explain the point estimate for differences in proportions between placebo and nicotine lozenges.

11. Conclusion Legitimacy for Nicotine Lozenge Effectiveness:

    • Use 4-sentence structure to explain and justify conclusion validity with statistical reasoning.

12. Generalization of Study Results:

    • Use 4-sentence structure to analyze generalization possibility of results for all smokers wanting to quit.