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1. Intro to Stats and Collecting Data(0)

Intro to Stats
(0)

Levels of Measurement
(0)

Intro to Collecting Data
(0)

Sampling Methods
(0)

2. Describing Data with Tables and Graphs(0)

Visualizing Qualitative vs. Quantitative Data
(0)

Frequency Distributions
(0)

Histograms
(0)

Bar Graphs and Pareto Charts
(0)

Pie Charts
(0)

Frequency Polygons
(0)

Dot Plots
(0)

Stemplots (Stem-and-Leaf Plots)
(0)

Time-Series Graph
(0)

3. Describing Data Numerically(0)

Mean
(0)

Median
(0)

Mode
(0)

Standard Deviation
(0)

Interpreting Standard Deviation
(0)

Percentiles & Quartiles
(0)

Describing Data Numerically Using a Graphing Calculator
(0)

Boxplots
(0)

Boxplots-Excel
(0)

4. Probability(0)

Basic Concepts of Probability
(0)

Complements
(0)

Addition Rule
(0)

Multiplication Rule: Independent Events
(0)

Introduction to Contingency Tables
(0)

Multiplication Rule: Dependent Events
(0)

Bayes' Theorem
(0)

Fundamental Counting Principle
(0)

Counting
(0)

5. Binomial Distribution & Discrete Random Variables(0)

Discrete Random Variables
(0)

Binomial Distribution
(0)

Finding Binomial Probabilities-Excel
(0)

Poisson Distribution
(0)

Finding Poisson Probabilities-Excel
(0)

Hypergeometric Distribution
(0)

6. Normal Distribution and Continuous Random Variables(0)

Uniform Distribution
(0)

Standard Normal Distribution
(0)

Probabilities & Z-Scores w/ Graphing Calculator
(0)

Non-Standard Normal Distribution
(0)

Finding Probabilities, Z Values, and X Values with the Normal Distribution-Excel
(0)

7. Sampling Distributions & Confidence Intervals: Mean(0)

Sampling Distribution of the Sample Mean and Central Limit Theorem
(0)

Distribution of Sample Mean - Excel
(0)

Introduction to Confidence Intervals
(0)

Confidence Intervals for Population Mean
(0)

Determining the Minimum Sample Size Required
(0)

Finding Probabilities and T Critical Values - Excel
(0)

Confidence Intervals for Population Means - Excel
(0)

8. Sampling Distributions & Confidence Intervals: Proportion(0)

Sampling Distribution of Sample Proportion
(0)

Confidence Intervals for Population Proportion
(0)

Confidence Intervals for Population Proportion - Excel
(0)

Chi Square Distribution
(0)

Confidence Intervals for Population Variance
(0)

9. Hypothesis Testing for One Sample(0)

Steps in Hypothesis Testing
(0)

Performing Hypothesis Tests: Means
(0)

Hypothesis Testing: Means - Excel
(0)

Performing Hypothesis Tests: Proportions
(0)

Hypothesis Testing: Proportions - Excel
(0)

Performing Hypothesis Tests: Variance
(0)

Critical Values and Rejection Regions
(0)

Link Between Confidence Intervals and Hypothesis Testing
(0)

Type I & Type II Errors
(0)

10. Hypothesis Testing for Two Samples(0)

Two Proportions
(0)

Two Proportions Hypothesis Test - Excel
(0)

Two Means - Unknown, Unequal Variance
(0)

Two Means - Unknown Variances Hypothesis Test - Excel
(0)

Two Means - Unknown, Equal Variance
(0)

Two Means - Unknown, Equal Variances Hypothesis Test - Excel
(0)

Two Means - Known Variance
(0)

Two Means - Sigma Known Hypothesis Test - Excel
(0)

Two Means - Matched Pairs (Dependent Samples)
(0)

Matched Pairs Hypothesis Test - Excel
(0)

Two Variances and F Distribution
(0)

Two Variances - Graphing Calculator
(0)

11. Correlation(0)

Scatterplots & Intro to Correlation
(0)

Correlation Coefficient
(0)

Creating Scatterplots and FInding Correlation Coefficient - Excel
(0)

Hypothesis Tests for Correlation Coefficient Using TI-84
(0)

Inferences for the Correlation Coefficient - Excel
(0)

12. Regression(0)

Linear Regression & Least Squares Method
(0)

Residuals
(0)

Coefficient of Determination
(0)

Regression Line Equation and Coefficient of Determination - Excel
(0)

Finding Residuals and Creating Residual Plots - Excel
(0)

Inferences for Slope
(0)

Enabling Data Analysis Toolpak
(0)

Regression Readout of the Data Analysis Toolpak - Excel
(0)

Prediction Intervals
(0)

Prediction Intervals - Excel
(0)

Multiple Regression - Excel
(0)

Quadratic Regression
(0)

Quadratic Regression - Excel
(0)

13. Chi-Square Tests & Goodness of Fit(0)

Goodness of Fit Test
(0)

Goodness of FIt Test Using TI-84
(0)

Goodness of Fit Test - Excel
(0)

Contingency Tables
(0)

Independence Tests
(0)

Homogeneity Tests
(0)

Using Matrices on a TI-84
(0)

Independence Test Using TI-84
(0)

Independence Tests - Excel
(0)

14. ANOVA(0)

Introduction to ANOVA
(0)

One-Way ANOVA - Excel
(0)

Multiple Comparisons: Tukey Test
(0)

Multiple Comparisons: Tukey-Kramer Test
(0)

Multiple Comparisons: Bonferoni Test
(0)

Two-Way ANOVA
(0)

Two-Way ANOVA - Excel
(0)

3. Describing Data Numerically

Standard Deviation

3. Describing Data Numerically

Standard Deviation: Videos & Practice Problems

Video Lessons Practice Worksheet

Back to all problems

28 of 0

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Problem 28Multiple Choice

A population consists of $\text{4 hours}$ , $\text{7 hours}$ , and $\text{15 hours}$ of study time per week, based on a student survey. Assume that samples of two values are randomly selected with replacement from this population and list all possible pairs.
For each of the nine possible samples, calculate the variance by:
Treating each sample as a population (dividing by n).
Treating each sample as a sample (dividing by n−1).
Finally, compute the mean of these variances in both cases.
Which approach results in values that are better estimates of the true population variance, and why?

Dividing by n is better because it ensures the variance is always slightly lower, making the estimate more stable.

Dividing by n−1 is better because it corrects for the bias that occurs when estimating population variance from a sample.

Both approaches give the same result, so it doesn’t matter whether you divide by n or n-1.

Neither approach provides a good estimate; a larger sample size is required to estimate variance accurately.

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