Collaborative statistics

OpenStax

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0.1 About connexions

0.2 About “collaborative statistics”

1 Additional resources

2 Author acknowledgements

3 Student welcome letter

Sampling and data

Sampling and data

6.1 Variation in data

6.2 Variation in samples

6.3 Size of a sample

6.4 Optional collaborative classroom exercise

6.5 Critical evaluation

7 Answers and rounding off

10 Practice: sampling and data

11.1 Try these multiple choice questions

12 Lab 1: data collection

13 Lab 2: sampling experiment

13.1 Student learning outcomes

13.2 A simple random sample

13.3 A systematic sample

13.4 A stratified sample

13.5 A stratified sample

13.6 A cluster sample

13.7 Restaurants stratified by city and entree cost

Descriptive statistics

Descriptive statistics

1 Displaying data

2 Stem and leaf graphs (stemplots), line graphs and bar graphs

3.1 Optional collaborative exercise

5 Measures of the location of the data

6 Measures of the center of the data

7 Skewness and the mean, median, and mode

8 Measures of the spread of the data

9 Summary of formulas

10 Practice 1: center of the data

11 Practice 2: spread of the data

12.1 Try these multiple choice questions (exercises 24 - 30).

13 Lab: descriptive statistics

Probability topics

Probability topics

0.1 Student learning outcomes

0.2 Introduction

0.3 Optional collaborative classroom exercise

2 Independent and mutually exclusive events

2.1 Independent events

2.2 Mutually exclusive events

3 Two basic rules of probability

3.1 The multiplication rule

3.2 The addition rule

4 Contingency tables

5 Venn diagrams (optional)

6 Tree diagrams (optional)

7 Summary of formulas

8 Practice 1: contingency tables

9 Practice 2: calculating probabilities

9.1 Student learning outcomes

9.3 Analyze the data

12 Lab: probability topics

Discrete random variables

Discrete random variables

1 Probability distribution function (pdf) for a discrete random variable

2 Mean or expected value and standard deviation

3 Common discrete probability distribution functions

5 Geometric (optional)

6 Hypergeometric (optional)

8 Summary of functions

9 Practice 1: discrete distribution

9.1 Student learning outcomes

9.3 Organize the data

9.4 Discussion question

10 Practice 2: binomial distribution

11 Practice 3: poisson distribution

12 Practice 4: geometric distribution

13 Practice 5: hypergeometric distribution

13.1 Student learning outcomes

13.3 Interpret the data

16 Lab 1: discrete distribution (playing card experiment)

17 Lab 2: discrete distribution (lucky dice experiment)

Continuous random variables

Continuous random variables

1 Continuous probability functions

2 The uniform distribution

3 The exponential distribution

3.1 Optional collaborative classroom activity

4 Summary of the uniform and exponential probability distributions

5 Practice 1: uniform distribution

5.1 Student learning outcomes

5.3 Describe the data

5.4 Probability distribution

5.5 Random probability

6 Practice 2: exponential distribution

9 Lab: continuous distribution

The normal distribution

The normal distribution

1 The standard normal distribution

3 Areas to the left and right of x

4 Calculations of probabilities

5 Summary of formulas

6 Practice: the normal distribution

6.1 Student learning outcomes

6.3 Normal distribution

9 Lab 1: normal distribution (lap times)

10 Lab 2: normal distribution (pinkie length)

The central limit theorem

The central limit theorem

1 The central limit theorem for sample means (averages)

2 The central limit theorem for sums

3 Using the central limit theorem

3.1 Examples of the central limit theorem

4 Summary of formulas

5 Practice: the central limit theorem

6.1 Try these multiple choice questions (exercises19 - 23).

8 Lab 1: central limit theorem (pocket change)

9 Lab 2: central limit theorem (cookie recipes)

Confidence intervals

Confidence intervals

1 Confidence interval, single population mean, population standard deviation

1.1 Calculating the confidence interval

1.2 Changing the confidence level or sample size

1.3 Working backwards to find the error bound or sample mean

1.4 Calculating the sample size n

2 Confidence interval, single population mean, standard deviation unknown

3 Confidence interval for a population proportion

3.1 Calculating the sample size n

4 Summary of formulas

5 Practice 1: confidence intervals for means, known population standard

6 Practice 2: confidence intervals for means, unknown population standard

7 Practice 3: confidence intervals for proportions

10 Lab 1: confidence interval (home costs)

11 Lab 2: confidence interval (place of birth)

12 Lab 3: confidence interval (womens' heights)

Hypothesis testing: single mean and single proportion

Hypothesis testing: single mean and single proportion

0.1 Student learning outcomes

0.2 Introduction

1 Null and alternate hypotheses

2 Outcomes and the type i and type ii errors

3 Distribution needed for hypothesis testing

6 Using the sample to test the null hypothesis

7 Decision and conclusion

8 Additional information

9 Summary of the hypothesis test

11 Summary of formulas

12 Practice 1: single mean, known population standard deviation

13 Practice 2: single mean, unknown population standard deviation

14 Practice 3: single proportion

15.1 Try these multiple choice questions.

17 Lab: hypothesis testing of a single mean and single proportion

Hypothesis testing: two means, paired data, two proportions

Hypothesis testing: two population means and two population proportions

0.1 Student learning outcomes

0.2 Introduction

1 Comparing two independent population means with unknown population

2 Comparing two independent population means with known population standard

3 Comparing two independent population proportions

4 Matched or paired samples

4.1 Matched or paired samples

5 Summary of types of hypothesis tests

6 Practice 1: hypothesis testing for two proportions

7 Practice 2: hypothesis testing for two averages

7.1 Student learning outcome

7.3 Hypothesis testing: two means

7.4 Discussion question

10 Lab: hypothesis testing for two means and two proportions

The chi-square distribution

The chi-square distribution

0.1 Student learning outcomes

0.2 Introduction

0.3 Optional collaborative classroom activity

2 Facts about the chi-square distribution

3 Goodness-of-fit test

4 Test of independence

5 The chi-square distribution: test for homogeneity

6 The chi-square distribution: comparison summary of the chi-square tests

7 Test of a single variance

8 Summary of formulas

9 Practice 1: goodness-of-fit test

10 Practice 2: contingency tables

11 Practice 3: test of a single variance

12.1 Word problems

12.2 Try these true/false questions.

14 Lab 1: chi-square goodness-of-fit

15 Lab 2: chi-square test for independence

Linear regression and correlation

Linear regression and correlation

1 Linear equations

2 Slope and y-intercept of a linear equation

3 Scatter plots

4 The regression equation

5 Correlation coefficient and coefficient of determination

6 Testing the significance of the correlation coefficient

9 95% critical values of the sample correlation coefficient table

11 Practice: linear regression

11.1 Student learning outcomes

11.5 Linear equation

11.8 Discussion questions

13 Lab 1: regression (distance from school)

14 Lab 2: regression (textbook cost)

15 Lab 3: regression (fuel efficiency)

F distribution and one-way anova

F distribution and one-way anova

0.1 Student learning outcomes

0.2 Introduction

1 One-way anova

1.1 F distribution and one-way anova: purpose and basic assumptions of one

1.2 The null and alternate hypotheses

2 The f distribution and the f ratio

3 Facts about the f distribution

4 Test of two variances

6 Practice: one-way anova

6.1 Student learning outcome

6.5 Decisions and conclusions

9 Lab: one-way anova

Practice final exam 1

1 Practice final exam 2

3 English phrases written mathematically

4 Symbols and their meanings

6 Notes for the ti-83, 83+, 84 calculator

6.2 Manipulating one-variable statistics

6.3 Drawing histograms

6.4 Linear regression

6.5 Sample data

6.6 Ti-83, 83+, 84 instructions for distributions and tests

6.7 Distributions

6.8 Tests and confidence intervals

Source: OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40

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