Table of contents

1. Intro to Stats and Collecting Data1h 14m

Intro to Stats
24m

Levels of Measurement
18m

Intro to Collecting Data
8m

Sampling Methods
23m

2. Describing Data with Tables and Graphs1h 56m

Visualizing Qualitative vs. Quantitative Data
4m

Frequency Distributions
35m

Histograms
14m

Bar Graphs and Pareto Charts
11m

Pie Charts
8m

Frequency Polygons
10m

Dot Plots
6m

Stemplots (Stem-and-Leaf Plots)
14m

Time-Series Graph
9m

3. Describing Data Numerically2h 5m

Mean
9m

Median
17m

Mode
7m

Standard Deviation
16m

Interpreting Standard Deviation
20m

Percentiles & Quartiles
14m

Describing Data Numerically Using a Graphing CalculatorBonus
10m

Boxplots
8m

Descriptive Statistics-ExcelBonus
11m

Boxplots-ExcelBonus
8m

4. Probability2h 17m

Basic Concepts of Probability
7m

Complements
6m

Addition Rule
17m

Multiplication Rule: Independent Events
11m

Introduction to Contingency Tables
17m

Multiplication Rule: Dependent Events
17m

Bayes' Theorem
13m

Fundamental Counting Principle
8m

Counting
37m

5. Binomial Distribution & Discrete Random Variables3h 6m

Discrete Random Variables
31m

Binomial Distribution
1h 7m

Finding Binomial Probabilities-ExcelBonus
17m

Poisson Distribution
40m

Finding Poisson Probabilities-ExcelBonus
15m

Hypergeometric Distribution
14m

6. Normal Distribution and Continuous Random Variables2h 11m

Uniform Distribution
18m

Standard Normal Distribution
39m

Probabilities & Z-Scores w/ Graphing CalculatorBonus
19m

Non-Standard Normal Distribution
21m

Finding Probabilities, Z Values, and X Values with the Normal Distribution-ExcelBonus
32m

7. Sampling Distributions & Confidence Intervals: Mean3h 23m

Sampling Distribution of the Sample Mean and Central Limit Theorem
19m

Distribution of Sample Mean - ExcelBonus
23m

Introduction to Confidence Intervals
15m

Confidence Intervals for Population Mean
1h 18m

Determining the Minimum Sample Size Required
12m

Finding Probabilities and T Critical Values - ExcelBonus
28m

Confidence Intervals for Population Means - ExcelBonus
25m

8. Sampling Distributions & Confidence Intervals: Proportion2h 10m

Sampling Distribution of Sample Proportion
29m

Confidence Intervals for Population Proportion
42m

Confidence Intervals for Population Proportion - ExcelBonus
12m

Chi Square Distribution
20m

Confidence Intervals for Population Variance
24m

9. Hypothesis Testing for One Sample5h 8m

Steps in Hypothesis Testing
1h 6m

Performing Hypothesis Tests: Means
1h 4m

Hypothesis Testing: Means - ExcelBonus
42m

Performing Hypothesis Tests: Proportions
37m

Hypothesis Testing: Proportions - ExcelBonus
27m

Performing Hypothesis Tests: Variance
12m

Critical Values and Rejection Regions
28m

Link Between Confidence Intervals and Hypothesis Testing
12m

Type I & Type II Errors
16m

10. Hypothesis Testing for Two Samples5h 37m

Two Proportions
1h 13m

Two Proportions Hypothesis Test - ExcelBonus
28m

Two Means - Unknown, Unequal Variance
1h 3m

Two Means - Unknown Variances Hypothesis Test - ExcelBonus
12m

Two Means - Unknown, Equal Variance
15m

Two Means - Unknown, Equal Variances Hypothesis Test - ExcelBonus
9m

Two Means - Known Variance
12m

Two Means - Sigma Known Hypothesis Test - ExcelBonus
21m

Two Means - Matched Pairs (Dependent Samples)
42m

Matched Pairs Hypothesis Test - ExcelBonus
12m

Two Variances and F Distribution
29m

Two Variances - Graphing CalculatorBonus
16m

11. Correlation1h 24m

Scatterplots & Intro to Correlation
26m

Correlation Coefficient
21m

Creating Scatterplots and FInding Correlation Coefficient - ExcelBonus
6m

Hypothesis Tests for Correlation Coefficient Using TI-84 Bonus
17m

Inferences for the Correlation Coefficient - ExcelBonus
11m

12. Regression3h 33m

Linear Regression & Least Squares Method
26m

Residuals
12m

Coefficient of Determination
12m

Regression Line Equation and Coefficient of Determination - ExcelBonus
8m

Finding Residuals and Creating Residual Plots - ExcelBonus
11m

Inferences for Slope
31m

Enabling Data Analysis ToolpakBonus
1m

Regression Readout of the Data Analysis Toolpak - ExcelBonus
21m

Prediction Intervals
13m

Prediction Intervals - ExcelBonus
19m

Multiple Regression - ExcelBonus
29m

Quadratic Regression
15m

Quadratic Regression - ExcelBonus
10m

13. Chi-Square Tests & Goodness of Fit2h 21m

Goodness of Fit Test
41m

Goodness of FIt Test Using TI-84Bonus
17m

Goodness of Fit Test - ExcelBonus
10m

Contingency Tables
12m

Independence Tests
14m

Homogeneity Tests
11m

Using Matrices on a TI-84Bonus
6m

Independence Test Using TI-84Bonus
12m

Independence Tests - ExcelBonus
13m

14. ANOVA2h 29m

Introduction to ANOVA
31m

One-Way ANOVA - ExcelBonus
12m

Multiple Comparisons: Tukey Test
14m

Multiple Comparisons: Tukey-Kramer Test
15m

Multiple Comparisons: Bonferoni Test
24m

Two-Way ANOVA
32m

Two-Way ANOVA - ExcelBonus
18m

1. Intro to Stats and Collecting Data

Intro to Stats

Statistics

1. Intro to Stats and Collecting Data

Intro to Stats

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2:16 minutes

Problem 10.CQQ.6

Textbook Question

Exercises 1–10 are based on the following sample data consisting of costs of dinner (dollars) and the amounts of tips (dollars) left by diners. The data were collected by students of the author.
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Change in Scale Exercise 1 stated that for the given paired data, r = 0.846. How does that value change if all of the amounts of dinners are left unchanged but all of the tips are expressed in cents instead of dollars?

Verified step by step guidance

Understand the problem: We are given a correlation coefficient (r = 0.846) for paired data of dinner costs and tips in dollars. We need to determine how this correlation changes if tips are converted from dollars to cents.

Recall the property of correlation: The correlation coefficient (r) is a measure of the strength and direction of a linear relationship between two variables. It is unitless and invariant to changes in scale or units of measurement.

Consider the effect of changing units: Converting tips from dollars to cents is a linear transformation (multiplying by 100). Such transformations do not affect the correlation coefficient because correlation is based on standardized values (z-scores) which are unaffected by changes in scale.

Conclude the effect on correlation: Since correlation is unaffected by linear transformations of the data, the correlation coefficient remains the same even if tips are expressed in cents instead of dollars.

Summarize the result: The value of the correlation coefficient (r = 0.846) does not change when the tips are converted from dollars to cents.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Correlation Coefficient (r)

The correlation coefficient, denoted as 'r', measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where values close to 1 or -1 indicate a strong linear relationship, and values near 0 suggest a weak linear relationship. In this context, r = 0.846 suggests a strong positive correlation between dinner costs and tips.

Scale Invariance of Correlation

Correlation is a scale-invariant measure, meaning it is unaffected by changes in the scale of measurement of the variables. This implies that multiplying all values of one variable by a constant (such as converting dollars to cents) does not change the correlation coefficient. Therefore, expressing tips in cents instead of dollars will not alter the value of r.

Linear Transformation

A linear transformation involves changing a variable by multiplying it by a constant and/or adding a constant. In this problem, converting tips from dollars to cents is a linear transformation (multiplying by 100). Such transformations do not affect the correlation coefficient, as correlation measures the relative, not absolute, changes between variables.

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