Higher Level for the IB Diploma Option Topic 7 Statistics

Introduction

1. Combining random variables

1A. Adding and multiplying all the data by a constant

1B. Adding independent random variables

1C. Expectation and variance of the sample mean and sample sum

1D. Linear combinations of normal variables

1E. The distribution of sums and averages of samples

2. More about statistical distributions

2A. Geometric distribution

2B. Negative binomial distribution

2C. Probability generating functions

2D. Using probability generating functions to find the distribution of the sum of discrete random variables

3. Cumulative distribution functions

3A. Finding the cumulative probability function

3B. Distributions of functions of a continuous random variable

4. Unbiased estimators and confidence intervals

4A. Unbiased estimates of the mean and variance

4B. Theory of unbiased estimators

4C. Confidence interval for the population mean

4D. The t-distribution

4E. Confidence interval for a mean with unknown variance

5. Hypothesis testing

5A. The principle of hypothesis testing

5B. Hypothesis testing for a mean with known variance

5C. Hypothesis testing for a mean with unknown variance

5D. Paired samples

5E. Errors in hypothesis testing

6. Bivariate distributions

6A. Introduction to discrete bivariate distributions

6B. Covariance and correlation

6C. Linear regression

7. Summary and mixed examination practice

Answers

Appendix: Calculator skills sheets

A CASIO. Finding probabilities in the t-distribution

A TEXAS. Finding probabilities in the t-distribution

B CASIO. Finding t-scores given probabilities

B TEXAS. Finding t-scores given probabilities

C CASIO. Confidence interval for the mean with unknown variance from data

C TEXAS. Confidence interval for the mean with unknown variance from data

D CASIO. Confidence interval for the mean with unknown variance from stats

D TEXAS. Confidence interval for the mean with unknown variance from stats

E CASIO. Hypothesis test for the mean with unknown variance from data

E TEXAS. Hypothesis test for the mean with unknown variance from data

F CASIO. Hypothesis test for the mean with unknown variance from stats

F TEXAS. Hypothesis test for the mean with unknown variance from stats

G CASIO. Confidence interval for the mean with known variance from data

G TEXAS. Confidence interval for the mean with known variance from data

H CASIO. Confidence interval for the mean with known variance from stats

H TEXAS. Confidence interval for the mean with known variance from stats

I CASIO. Hypothesis test for the mean with known variance from stats

I TEXAS. Hypothesis test for the mean with known variance from stats

J CASIO. Finding the correlation coefficient and the equation of the regression line

J TEXAS. Finding the correlation coefficient and the equation of the regression line

Glossary

Index