Introductory statistics

OpenStax

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0.1 About Introductory Statistics

0.2 Coverage and scope

0.3 Alternate sequencing

0.4 Pedagogical foundation and features

0.5 Statistics labs

0.6 Ancillaries

0.7 About our team

0.8 Senior contributing authors

0.9 Contributing authors

0.10 Sample ti technology

1 Review exercises (ch 3-13)

1.10 Chapter 12

1.11 Chapter 13

1.20 Chapter 10

1.21 Chapter 11

1.22 Chapter 12

1.23 Chapter 13

1.24 References

2 Practice tests (1-4) and final exams

2.1 Practice test 1

2.2 1.1: definitions of statistics, probability, and key terms

2.3 1.2: data, sampling, and variation in data and sampling

2.4 1.3: frequency, frequency tables, and levels of measurement

2.5 1.4: experimental design and ethics

2.6 2.1: stem-and leaf graphs (stemplots), line graphs, and bar graphs

2.7 2.2: histograms, frequency polygons, and time series graphs

2.8 2.3: measures of the location of the data

2.9 2.4: box plots

2.10 2.5: measures of the center of the data

2.11 2.6: skewness and the mean, median, and mode

2.12 2.7: measures of the spread of the data

2.13 3.1: terminology

2.14 3.2: independent and mutually exclusive events

2.15 3.3: two basic rules of probability

2.16 3.4: contingency tables

2.17 3.5: tree and venn diagrams

2.18 Practice test 1 solutions

2.19 1.1: definitions of statistics, probability, and key terms

2.20 1.2: data, sampling, and variation in data and sampling

2.21 1.3: frequency, frequency tables, and levels of measurement

2.22 1.4: experimental design and ethics

2.23 2.1: stem-and leaf graphs (stemplots), line graphs, and bar graphs

2.24 2.2: histograms, frequency polygons, and time series graphs

2.25 2.3: measures of the location of the data

2.26 2.4: box plots

2.27 2.5: measures of the center of the data

2.28 2.6: skewness and the mean, median, and mode

2.29 2.7: measures of the spread of the data

2.30 3.1: terminology

2.31 3.2: independent and mutually exclusive events

2.32 3.3: two basic rules of probability

2.33 3.4: contingency tables

2.34 3.5: tree and venn diagrams

2.35 Practice test 2

2.36 4.1: probability distribution function (pdf) for a discrete random

2.37 4.2: mean or expected value and standard deviation

2.38 4.3: binomial distribution

2.39 4.4: geometric distribution

2.40 4.5: hypergeometric distribution

2.41 4.6: poisson distribution

2.42 5.1: continuous probability functions

2.43 5.2: the uniform distribution

2.44 5.3: the exponential distribution

2.45 6.1: the standard normal distribution

2.46 6.2: using the normal distribution

2.47 7.1: the central limit theorem for sample means (averages)

2.48 7.2: the central limit theorem for sums

2.49 7.3: using the central limit theorem

2.50 Practice test 2 solutions

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

2.52 Mean or expected value and standard deviation

2.53 Binomial distribution

2.54 4.4: geometric distribution

2.55 4.5: hypergeometric distribution

2.56 4.6: poisson distribution

2.57 5.1: continuous probability functions

2.58 5.2: the uniform distribution

2.59 5.3: the exponential distribution

2.60 6.1: the standard normal distribution

2.61 6.2: using the normal distribution

2.62 7.1: the central limit theorem for sample means (averages)

2.63 7.2: the central limit theorem for sums

2.64 7.3: using the central limit theorem

2.65 Practice test 3

2.66 8.1: confidence interval, single population mean, population standard

2.67 8.2: confidence interval, single population mean, standard deviation

2.68 8.3: confidence interval for a population proportion

2.69 9.1: null and alternate hypotheses

2.70 9.2: outcomes and the type i and type ii errors

2.71 9.3: distribution needed for hypothesis testing

2.72 9.4: rare events, the sample, decision, and conclusion

2.73 9.5: additional information and full hypothesis test examples

2.74 10.1: comparing two independent population means with unknown population

2.75 10.2: comparing two independent population means with known population

2.76 10.3: comparing two independent population proportions

2.77 10.4: matched or paired samples

2.78 11.1: facts about the chi-square distribution

2.79 11.2: goodness-of-fit test

2.80 11.3: test of independence

2.81 11.4: test of homogeneity

2.82 11.5: comparison summary of the chi-square tests: goodness-of-fit,

2.83 11.6: test of a single variance

2.84 Practice test 3 solutions

2.85 8.1: confidence interval, single population mean, population standard

2.86 8.2: confidence interval, single population mean, standard deviation

2.87 8.3: confidence interval for a population proportion

2.88 9.1: null and alternate hypotheses

2.89 9.2: outcomes and the type i and type ii errors

2.90 9.3: distribution needed for hypothesis testing

2.91 9.4: rare events, the sample, decision, and conclusion

2.92 9.5: additional information and full hypothesis test examples

2.93 10.1: comparing two independent population means with unknown population

2.94 10.2: comparing two independent population means with known population

2.95 10.3: comparing two independent population proportions

2.96 10.4: matched or paired samples

2.97 11.1: facts about the chi-square distribution

2.98 11.2: goodness-of-fit test

2.99 11.3: test of independence

2.100 11.4: test of homogeneity

2.101 11.5: comparison summary of the chi-square tests: goodness-of-fit,

2.102 11.6: test of a single variance

2.103 Practice test 4

2.104 12.1 linear equations

2.105 12.2: slope and Y -intercept of a linear equation

2.106 12.3: scatter plots

2.107 12.4: the regression equation

2.108 12.5: correlation coefficient and coefficient of determination

2.109 12.6: testing the significance of the correlation coefficient

2.110 12.7: prediction

2.111 12.8: outliers

2.112 13.1: one-way anova

2.113 13.2: the F Distribution

2.114 13.3: facts about the F Distribution

2.115 13.4: test of two variances

2.116 Practice test 4 solutions

2.117 12.1 linear equations

2.118 12.2: slope and y-intercept of a linear equation

2.119 12.3: scatter plots

2.120 12.4: the regression equation

2.121 12.5: correlation coefficient and coefficient of determination

2.122 12.6: testing the significance of the correlation coefficient

2.123 12.7: prediction

2.124 12.8: outliers

2.125 13.1: one-way anova

2.126 13.2: the F Distribution

2.127 13.3: facts about the F Distribution

2.128 13.4: test of two variances

2.129 Practice final exam 1

2.130 Practice final exam 1 solutions

2.131 Solutions

2.132 Practice final exam 2

2.133 Practice final exam 2 solutions

2.134 Solutions

4 Group and partner projects

5 Solution sheets

5.1 Hypothesis testing with one sample

5.2 Hypothesis testing with two samples

5.3 The chi-square distribution

5.4 F distribution and one-way anova

6 Mathematical phrases, symbols, and formulas

7 Notes for the ti-83, 83+, 84, 84+ calculators

Sampling and data

1 Definitions of statistics, probability, and key terms

1.1 Probability

1.4 Chapter review

2 Data, sampling, and variation in data and sampling

2.1 Qualitative data discussion

2.2 Percentages that add to more (or less) than 100%

2.3 Omitting categories/missing data

2.4 Pie charts: no missing data

2.6 Variation in data

2.7 Variation in samples

2.8 Size of a sample

2.9 Critical evaluation

2.10 References

2.11 Chapter review

2.13 Bringing it together

3 Frequency, frequency tables, and levels of measurement

3.1 Answers and rounding off

3.2 Levels of measurement

3.5 Chapter review

4 Experimental design and ethics

4.3 Chapter review

5 Data collection experiment

6 Sampling experiment

Descriptive statistics

1 Stem-and-leaf graphs (stemplots), line graphs, and bar graphs

2 Histograms, frequency polygons, and time series graphs

3 Measures of the location of the data

3.1 A formula for finding the k Th percentile

3.2 A formula for finding the percentile of a value in a data set

3.3 Interpreting percentiles, quartiles, and median

3.5 Chapter review

3.6 Formula review

5 Measures of the center of the data

6 Skewness and the mean, median, and mode

7 Measures of the spread of the data

7.1 The standard deviation

7.2 The standard deviation provides a measure of the overall variation in

7.3 The standard deviation can be used to determine whether a data value is

7.4 Calculating the standard deviation

7.5 Formulas for the sample standard deviation

7.6 Formulas for the population standard deviation

7.7 Sampling variability of a statistic

7.8 Explanation of the standard deviation calculation shown in the table

7.9 Standard deviation of grouped frequency tables

7.10 Comparing values from different data sets

7.11 References

7.12 Chapter review

7.13 Formula review

7.14 Bringing it together

8 Descriptive statistics

Probability topics

1.2 Chapter review

1.3 Formula review

2 Independent and mutually exclusive events

2.1 Independent events

2.2 Mutually exclusive events

2.4 Chapter review

2.5 Formula review

2.6 Bringing it together

3 Two basic rules of probability

4 Contingency tables

5 Tree and venn diagrams

5.1 Tree diagrams

5.2 Venn diagram

5.4 Chapter review

5.5 Bringing it together

6 Probability topics

Discrete random variables

0.1 Random variable notation

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

2 Mean or expected value and standard deviation

3 Binomial distribution

3.1 Notation for the binomial: B = binomial probability distribution function

3.3 Chapter review

3.4 Formula review

4 Geometric distribution

4.1 Notation for the geometric: g = geometric probability distribution

4.3 Chapter review

4.4 Formula review

5 Hypergeometric distribution

5.1 Notation for the hypergeometric: h = hypergeometric probability distribution

5.2 Chapter review

5.3 Formula review

6 Poisson distribution

6.1 Notation for the poisson: p = poisson probability distribution function

6.3 Chapter review

6.4 Formula review

7 Discrete distribution (playing card experiment)

8 Discrete distribution (lucky dice experiment)

Continuous random variables

1 Continuous probability functions

2 The uniform distribution

3 The exponential distribution

4 Continuous distribution

The normal distribution

0.1 Formula review

1 The standard normal distribution

2 Using the normal distribution

2.1 Calculations of probabilities

2.3 Chapter review

2.4 Formula review

3 Normal distribution (lap times)

4 Normal distribution (pinkie length)

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

4 Central limit theorem (pocket change)

5 Central limit theorem (cookie recipes)

Confidence intervals

1 A single population mean using the normal distribution

1.1 Calculating the confidence interval

1.2 Calculating the confidence interval

1.3 Finding the z -score for the stated confidence level

1.4 Calculating the error bound ( EBM )

1.5 Constructing the confidence interval

1.6 Writing the interpretation

1.7 Changing the confidence level or sample size

1.8 Working backwards to find the error bound or sample mean

1.9 Calculating the sample size n

1.10 References

1.11 Chapter review

1.12 Formula review

2 A single population mean using the student t distribution

2.2 Chapter review

2.3 Formula review

3 A population proportion

3.1 “plus four” confidence interval for p

3.2 Calculating the sample size n

3.4 Chapter review

3.5 Formula review

4 Confidence interval (home costs)

5 Confidence interval (place of birth)

6 Confidence interval (women's heights)

Hypothesis testing with one sample

1 Null and alternative hypotheses

2 Outcomes and the type i and type ii errors

3 Distribution needed for hypothesis testing

3.1 Assumptions

3.2 Chapter review

3.3 Formula review

4 Rare events, the sample, decision and conclusion

4.1 Rare events

4.2 Using the sample to test the null hypothesis

4.3 Decision and conclusion

4.4 Chapter review

5 Additional information and full hypothesis test examples

6 Hypothesis testing of a single mean and single proportion

Hypothesis testing with two samples

1 Two population means with unknown standard deviations

2 Two population means with known standard deviations

3 Comparing two independent population proportions

3.2 Chapter review

3.3 Formula review

4 Matched or paired samples

5 Hypothesis testing for two means and two proportions

The chi-square distribution

1 Facts about the chi-square distribution

2 Goodness-of-fit test

2.2 Chapter review

2.3 Formula review

3 Test of independence

4 Test for homogeneity

5 Comparison of the chi-square tests

5.1 Chapter review

5.2 Bringing it together

6 Test of a single variance

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

8 Lab 2: chi-square test of independence

Linear regression and correlation

1 Linear equations

2 Scatter plots

2.1 Chapter review

3 The regression equation

4 Testing the significance of the correlation coefficient

6.1 Identifying outliers

6.2 Numerical identification of outliers

6.3 How does the outlier affect the best fit line?

6.4 Numerical identification of outliers: calculating s And finding outliers

6.5 95% critical values of the sample correlation coefficient table

6.7 Chapter review

7 Regression (distance from school)

8 Regression (textbook cost)

9 Regression (fuel efficiency)

F distribution and one-way anova

1 One-way anova

1.1 The null and alternative hypotheses

1.2 Chapter review

2 The f distribution and the f-ratio

3 Facts about the f distribution

4 Test of two variances

5 Lab: one-way anova

Source: OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18

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