Unit 11 - Statistics Option

Unit Objectives
By the end of this unit students should be able to:
·        Find and use cumulative distribution functions for both discrete and continuous distributions.
·         Solve problems using the geometric distribution and negative binomial distribution
·         Find and use probability generating functions and their properties
·         Solve problems involving linear combinations of random variables, their expectations and variances
·         Find and use unbiased estimators and estimates
·         Know and use the Central Limit Theorem
·         Find confidence intervals for the mean of  a normal population
·         Carry out one and two tailed hypothesis tests.
·         Identify and find probabilities of Type I and Type II errors
·         Calculate the covariance and (population and sample) product moment correlation coefficient for bivariate data
·         Interpret r and R in terms of correlation
·         Use the t statistic to test the null hypothesis ρ = 0
·         Know the facts that the regression of X on Y and Y on X are linear
·         Calculate least-squares estimates of these regression lines
·         Use regression lines to make predictions
Lesson Resources​
1. Cumulative Distribution Functions
2. Geometric Distribution
3. Linear Combinations of Random Variables
4. ​Sample Means
5. Linear Combinations of Normal Distributions
6. Sample Means and Normal Distributions
7. ​Central Limit Theorem
8. Negative Binomial Distribution
9. Probability Generator Functions
10. Probability Generator Functions 2
11. Unbiased Estimators of Mean and Variance
12. Unbiased Estimators
13. Confidence Intervals
14. The t-Distribution
15. Confidence Intervals with Unknown Variance
16. Introduction to Hypothesis Testing
17. Critical Regions
18. p-values
19. Z-Tests
20. T-Tests
21. Paired Samples
22. Errors in Hypothesis Testing
23. Bivariate Distributions
24. Covariance and Rho
25. Hypothesis Testing for Rho
26. Linear Regression
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