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

7 Answers and rounding off

10 Practice: sampling and data

11.1 Try these multiple choice questions

12 Lab 1: data collection

12.1 Student learning outcomes

12.2 Movie survey

12.3 Order the data

12.4 Discussion questions

13 Lab 2: sampling experiment

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

13 Lab: descriptive statistics

Probability topics

Probability topics

2 Independent and 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

7.2 Addition rule

7.3 Mutually exclusive

7.4 Multiplication rule

7.5 Independence

8 Practice 1: contingency tables

9 Practice 2: calculating probabilities

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

10 Practice 2: binomial distribution

11 Practice 3: poisson distribution

12 Practice 4: geometric distribution

13 Practice 5: hypergeometric distribution

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

4 Summary of the uniform and exponential probability distributions

5 Practice 1: uniform distribution

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

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

5.1 Student learning outcomes

5.3 Distribution

5.4 Graphing probability

5.5 Discussion question

8 Lab 1: central limit theorem (pocket change)

8.1 Student learning outcomes:

8.2 Collect the data

8.3 Collecting averages of pairs

8.4 Collecting averages of groups of five

8.5 Discussion questions

9 Lab 2: central limit theorem (cookie recipes)

Confidence intervals

Confidence intervals

1 Confidence interval, single population mean, population standard deviation

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

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

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

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

10 Lab: hypothesis testing for two means and two proportions

The chi-square distribution

The chi-square distribution

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

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

4.1 Optional collaborative classroom activity

4.2 Using the ti-83+ and ti-84+ calculators

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

12.1 Try these multiple choice 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

1 One-way anova

2 The f distribution and the f ratio

3 Facts about the f distribution

4 Test of two variances

6 Practice: one-way anova

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

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

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