Intro Statistics — Inference and Regression flashcards

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The second half of a college intro statistics course: the central limit theorem, confidence intervals, one- and two-sample z and t tests, p-values and errors, chi-square tests, correlation and least-squares regression, and one-way ANOVA with the F distribution.

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Learn 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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What is the most common misreading of the central limit theorem?

Thinking it makes the data normal. The CLT is about the sampling distribution of the sample mean: a big sample from a skewed population still looks skewed, but the means of many such samples pile up in a bell shape.
The Central Limit Theorem
Exam scores have a mean of 70 and an SD of 12. For random samples of 36 students, what are the mean and standard error of $\bar{x}$ ⁠?

The sampling distribution is centered at 70, with standard error $\frac{\sigma}{\sqrt{n}} = \frac{12}{6} = 2$ points.
The Central Limit Theorem
A 95% confidence interval for mean commute time is 22 to 28 minutes. Does that mean 95% of commuters take 22 to 28 minutes?

No. The interval estimates the population mean, not individual commutes. Individual times are far more spread out than the uncertainty about their average.
Confidence Intervals
A news report gives a 95% confidence interval of 0.38 to 0.46 for a proportion. What are the point estimate and the margin of error?

The point estimate is the midpoint, 0.42, and the margin of error is half the width, 0.04.
Confidence Intervals
A researcher says, "p = 0.04, so there is a 4% chance the null hypothesis is true." What is wrong?

A p-value is computed assuming H₀ is true: it is the probability of data at least as extreme as those observed. It is not the probability that H₀ is true, which classical tests never calculate.
Hypothesis Testing with One Sample › Logic and Errors
A test statistic is z = 1.80. Do you reject H₀ at α = 0.05 in a right-tailed test? In a two-tailed test?

Right-tailed: reject, since 1.80 > 1.645 (p ≈ 0.036). Two-tailed: do not reject, since 1.80 < 1.96 (p ≈ 0.072).
Hypothesis Testing with One Sample › Logic and Errors
Five students' score changes (after − before) are 3, 5, −1, 4 and 4. Test whether the mean change is positive.

Work with the differences: $\bar{d} = 3$ and $s_d \approx 2.35$ ⁠, so $t = \frac{3}{2.35 / \sqrt{5}} \approx 2.86$ with 4 df, giving p ≈ 0.023 one-sided.
Hypothesis Testing with Two Samples
Why is a chi-square test of goodness of fit or independence right-tailed?

The statistic $\sum \frac{(O - E)^2}{E}$ squares every gap, so it can never be negative, and only large values signal disagreement with H₀.
The Chi-Square Distribution
The correlation between hours of TV watched and GPA among students is r = −0.85. How do you describe it?

A strong negative linear association: students who watch more TV tend to have lower GPAs. It does not show that TV lowers GPA.
Linear Regression and Correlation
What does an F distribution look like?

It takes only nonnegative values, is skewed right, and is defined by two degrees of freedom (numerator and denominator). As both grow, it concentrates more tightly around 1.
F Distribution and One-Way ANOVA

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

Checked against:

OpenStax Introductory Statistics 2e, consulted as a reference; no text copied.
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