Exam Rules and Preparation

Exam Format and Allowed Materials

• Exam Platform: The exam is administered in-person through MyStatLab. Students must bring their laptops to class.

• Open Book Policy: The exam is open book and open Excel. Students may pre-populate formulas, create templates, and add notes in Excel.

• Permitted Tools: Only Excel and a handheld calculator are allowed. No other programs or browser windows may be open.

• Exam Integrity: Violations of the rules (e.g., opening unauthorized programs) will result in an automatic zero.

• Completion Procedure: Students must check in with the instructor before leaving the classroom to verify submission.

Overview of Material Covered

• Chapters Covered: 1, 2, 4, and 5

• Preparation Advice: Review homework problems for these chapters.

Chapter 1: Introduction to Statistics

Key Concepts to Identify

• Population vs. Sample: The population is the entire group of interest, while a sample is a subset of the population used for analysis.

• Experimental Unit: The object or individual on which a measurement is taken.

• Types of Data: Quantitative data are numerical (e.g., height, income), while qualitative data are categorical (e.g., color, type).

• Data Collection Methods: Includes survey, designed experiment, and observational study.

• Inferential vs. Descriptive Statistics: Descriptive statistics summarize data, while inferential statistics draw conclusions about a population based on a sample.

Chapter 2: Describing Data

Qualitative Data

• Frequency Table: A table that displays the count (frequency) and relative frequency of each category.

• Bar Chart: A graphical representation of categorical data with bars representing frequencies.

• Pie Chart: A circular chart divided into sectors representing relative frequencies.

• Excel Application: Know how to create and interpret these charts in Excel.

Quantitative Data

• Histogram: A bar graph representing the frequency distribution of numerical data, with bins for intervals.

• Interpretation: Analyze the shape (e.g., symmetric, right-skewed, left-skewed) and identify outliers or unusual features.

• Excel Application: Know how to create and interpret histograms in Excel.

Measures of Central Tendency

• Mean: The arithmetic average of a data set.

• Median: The middle value when data are ordered.

• Mode: The most frequently occurring value.

• Excel Functions: =AVERAGE() for mean, =MEDIAN() for median.

Measures of Variability

• Range: Difference between the maximum and minimum values.

• Variance: The average of squared deviations from the mean.

• Standard Deviation: The square root of the variance; measures spread.

• Excel Function: =STDEV() for standard deviation.

• Interpretation: Higher standard deviation indicates more variability.

Relationship Between Mean and Median

• Mean < Median: Distribution is left-skewed.

• Mean > Median: Distribution is right-skewed.

• Mean ≈ Median: Distribution is symmetric.

Chebychev's Theorem and Empirical Rule

These rules describe the spread of data around the mean.

• Empirical Rule: For symmetric, bell-shaped distributions, about 68% of data fall within 1 standard deviation, 95% within 2, and 99.7% within 3.

• Chebychev's Theorem: Applies to any distribution shape; at least 75% of data fall within 2 standard deviations, at least 89% within 3.

• Example: If mean = 70, standard deviation = 10, at least 75% of data are between 50 and 90 (using Chebychev's for 2 SDs).

Percentiles, Boxplots, and Z-scores

• Percentile: The kth percentile is the value below which k% of data fall.

• Boxplot: A graphical summary showing the median, quartiles, and possible outliers. The longer whisker indicates skewness direction.

• Z-score: Indicates how many standard deviations a value is from the mean.

Formula for Z-score:

• Interpretation: Z-scores above 0 are above the mean; below 0 are below the mean.

Chapter 4: Probability Distributions

Binomial Distribution

• Definition: The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success.

• Mean and Standard Deviation:

• Excel Functions: BINOM.DIST(x, n, p, FALSE) for exact probability; BINOM.DIST(x, n, p, TRUE) for cumulative probability.

• Example: If 15% of students go to grad school and 60 are sampled, expected number is .

Normal Distribution

• Definition: The normal distribution is a continuous, symmetric, bell-shaped distribution defined by its mean and standard deviation.

• Excel Functions:

  • P(X ≤ x): NORM.DIST(x, mean, sd, TRUE)

  • P(X > x):

  • P(a < X < b):

  • Given probability, find x: NORM.INV(probability, mean, sd)

• Standard Normal: A normal distribution with mean 0 and standard deviation 1. Z-scores are used to standardize values.

• Example: If exam grades are normally distributed with mean 82 and SD 6.2, probability a student scores between 80 and 90 is found using the above Excel functions.

Chapter 5: Sampling Distributions

Sampling Distribution of the Mean

• Definition: The sampling distribution of the sample mean is the probability distribution of all possible sample means from a population.

• Central Limit Theorem: For large samples, the sampling distribution of the mean is approximately normal, regardless of the population's distribution.

• Mean and Standard Error:

• Application: Allows calculation of probabilities about the sample mean using the normal distribution.

• Example: For a sample of 36 students with mean 82 and SD 6.2, probability the average score is higher than 84 is found using the sampling distribution formulas.