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Intro Statistics — Practice Questions flashcards

6 of 55 questions free to study here · 13 topics · the whole deck is built into Willys

Multiple-choice practice questions, one best answer each, on sampling and design, descriptive statistics, probability models, the normal curve, intervals, tests, chi-square, regression and ANOVA.

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Practice deck · part of Introductory Statistics · written against: Standard one-semester intro statistics course; OpenStax Introductory Statistics 2e, consulted as a reference; no text copied. Updated 2026-10-10.

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  1. A radio host invites listeners to call in and say whether the city should build a new stadium. Of 400 callers, 78% say no. What is the main problem with using 78% as an estimate of city-wide opinion?

    A) Sampling error is large, and more callers would remove it
    B) The stadium question must have been worded to lead callers
    C) Callers chose themselves, so strong opinions are overrepresented
    D) A sample of 400 is too small to estimate any proportion
    C) Callers chose themselves, so strong opinions are overrepresented

    This is a voluntary response sample: people with strong feelings are the most likely to call, so the sample is biased. More callers would not fix a bias; a random sample of residents would.
    Sampling and Data
  2. Of 200 surveyed students, 120 live on campus and 90 of those eat breakfast daily. Of the 80 who live off campus, 40 eat breakfast daily. A student who eats breakfast daily is chosen at random. What is the probability that the student lives on campus?

    A) 0.45
    B) 0.69
    C) 0.75
    D) 0.60
    B) 0.69

    Condition on breakfast eaters: there are 90 + 40 = 130, and 90 live on campus, so P(on campus | breakfast) = 90/130 ≈ 0.69. The tempting 0.75 is the reverse conditional, P(breakfast | on campus) = 90/120.
    Probability Topics
  3. Adult heights in a population are approximately normal with mean 170 cm and SD 8 cm. Using the empirical rule, about what percentage are taller than 186 cm?

    A) 2.5%
    B) 16%
    C) 0.15%
    D) 5%
    A) 2.5%

    186 cm is 2 SDs above the mean. About 95% lie within 2 SDs, leaving 5% split between the two tails, so about 2.5% are taller. The 5% counts both tails.
    The Normal Distribution
  4. From a random sample of undergraduates, a 95% confidence interval for mean nightly sleep is 6.4 to 7.2 hours. Which interpretation is correct?

    A) 95% of all possible samples have a mean between 6.4 and 7.2 hours
    B) About 95% of undergraduates sleep between 6.4 and 7.2 hours a night
    C) We are 95% confident that the mean for all undergraduates is in this range
    D) There is a 95% chance that the sample mean lies between 6.4 and 7.2
    C) We are 95% confident that the mean for all undergraduates is in this range

    The interval estimates the population mean; 95% confidence means the method captures μ in 95% of samples. It says nothing about individual students, and the sample mean (6.8) is certainly inside it.
    Confidence Intervals
  5. A survey records each student's class year (first-year to senior) and preferred study spot (library, dorm or café). Which procedure tests whether study-spot preference is related to class year?

    A) A chi-square goodness-of-fit test
    B) A one-way ANOVA on the study spots
    C) A two-sample t test on class years
    D) A chi-square test of independence
    D) A chi-square test of independence

    Both variables are categorical and come from one sample, so a two-way table and a test of independence fit. Goodness of fit compares a single categorical variable with a claimed distribution.
    The Chi-Square Distribution
  6. An agronomist compares mean crop yield across plots treated with 4 different fertilizers. Which procedure tests whether all four mean yields are equal in one test?

    A) Six separate two-sample t tests
    B) A paired t test on the four groups
    C) A one-way ANOVA F test
    D) A chi-square test of independence
    C) A one-way ANOVA F test

    One-way ANOVA compares several means in a single test at one significance level. Six separate t tests would push the chance of at least one false positive well above α.
    F Distribution and One-Way ANOVA

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About these cards

Review status: Second-reader reviewed, with corrections applied.

Checked against:

  • OpenStax Introductory Statistics 2e, consulted as a reference; no text copied.
  • Every numerical answer, distractor and critical value was recomputed by script.
  • Original questions written for this deck with hypothetical data; no official, textbook or question-bank items were copied.

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