Midterm study guide

Course

STAT218

Updated

June 13, 2026

The information below provides an overview of the midterm: what it covers, how to prepare, and the format. The midterm takes place in class on Thursday, May 7.

Scope

The midterm covers the following topics:

  1. Study design and data semantics

    • observational studies and experiments
    • sampling and study units
    • variable types (quantitative/categorical, explanatory/response)

  2. Descriptive statistics

    • graphical summaries (histograms, boxplots)
    • measures of center (mean, median) and spread (standard deviation, IQR)
    • shape, skew, and outliers

  3. Point estimation and sampling variability

    • sample statistics as estimates of population parameters
    • sampling distributions and standard error

  4. Confidence intervals for a mean

    • construction using the \(t\) distribution
    • interpretation in context
    • effect of sample size and confidence level on interval width

  5. One-sample \(t\)-tests

    • two-sided, upper-sided, and lower-sided alternatives
    • \(t\) statistic and \(p\)-value
    • confidence intervals
    • test-interval duality

  6. Two-sample \(t\)-tests

    • comparing two independent group means
    • two-sided, upper-sided, and lower-sided alternatives
    • confidence intervals for the difference in means

  7. One-way ANOVA

    • hypotheses comparing many group means
    • partitioning variation (MSG, MSE) and the \(F\) statistic
    • ANOVA table and \(p\)-value
    • effect size (\(\eta^2\))

Throughout, you should be familiar with the following core concepts:

  • statistical hypotheses and the testing framework
  • test statistics and \(p\)-values
  • type I and type II errors and the level of a test
  • conventional style for reporting results in context

Conventional reporting style

Results should be reported using precise, context-specific language. The templates below illustrate the expected style.

Point estimate

The mean total HDL cholesterol among the U.S. adult population is estimated to be 5.043 mmol/L (SE 0.0191).

Confidence interval

With 95% confidence, the mean total cholesterol among U.S. adults is estimated to be between 5.006 and 5.080 mmol/L.

Hypothesis test (one-sample \(t\)-test; two-sided)

The data do not provide evidence that the mean body temperature differs from 98.6°F (T = −1.328 on 38 degrees of freedom, p = 0.192).

The data provide evidence that the average U.S. adult does not sleep 8 hours per night (T = −42.53 on 3178 degrees of freedom, p < 0.0001).

Note that the test statistic, degrees of freedom, and \(p\)-value are always reported parenthetically, and the interpretation is stated in terms of the research question rather than in terms of the hypotheses themselves.

Format

The midterm is an in-class, closed-computer assessment. Quantitative results will be provided for each problem; prompts will ask you to interpret results in context or carry out simple follow-up calculations.

You may consult any of your course notes and are encouraged to bring a calculator. Digital devices are not permitted.

My recommendation: prepare a concise one- to two-page reference sheet covering key formulas, definitions, and result templates, and bring printed copies of any class notes you find useful.

Preparation

I recommend reviewing the following:

  1. Lecture slides and notes
  2. Textbook readings
Topic V&H sections
Study design and data semantics 1.1–1.5
Descriptive statistics 1.4–1.5
Point estimation and sampling variability 4.1
Confidence intervals 4.2
One-sample \(t\)-tests 4.3
Two-sample \(t\)-tests 5.2–5.3
One-way ANOVA 5.5
  1. Lab activities and homework assignments
  2. Example problems from the relevant textbook sections