**Available Skills for Statistics Foundations**

Institutions can select the skills to be included in the studentsâ€™ assessment. Students are only tested on selected skills. Statistics Foundations consists of one or more questions to assess each skill and instructional web pages to teach and review each skill.

## Probability

- Calculate the probability of an event
- Use the relation Pr(not A) = 1 - Pr(A)
- Recognize when events are mutually exclusive
- Apply Pr(A or B) = Pr(A) + Pr(B) for mutually exclusive events
- Apply Pr(A or B) = Pr(A) + Pr(B) - Pr(A & B)
- Recognize when events are independent
- Apply Pr(A and B) = Pr(A)Pr(B) for independent events
- Interpret the Pr(A|B) notation
- Apply Pr(A|B) = Pr(A) for independent events
- Calculate Pr(A|B) if A and B are not independent

## Descriptive

- Calculate the mean (discrete trials)
- Calculate the median (discrete trials)
- Calculate the mode (discrete trials)
- Calculate the variance (discrete trials)
- Calculate the standard deviation (discrete trials sample)
- Calculate the standard deviation (population)
- Calculate a weighted average
- Define the term 'expected value'
- Read a histogram with absolute frequencies
- Read a histogram with relative frequencies
- Estimate a percentile statistic from a histogram
- Distinguish between a sample and a population
- Explain what sample bias is

## Distributions

- Distinguish a discrete and a continuous distribution
- Distinguish a p.m.f. and a p.d.f.
- Calculate the probability from a p.m.f.
- Calculate probability from a p.d.f.
- Recognize the effect on a distribution plot of changing the mean
- Recognize the effect on a distribution plot of changing the std dev
- Distinguish median and mean on a distribution plot
- Identify a plot of a Normal distribution
- Calculate probability that a normal rand var is in certain range
- Define z-value
- Recognize probabilities corresponding to z-values 1, 2, 3
- Recognize z-values corresponding to probabilities 90%, 95%, 99%
- Apply the Central Limit Theorem
- Predict distribution of a sum or average of several independent rand vars
- Recognize a Bernoulli random variable
- Recognize a uniform distribution
- Recognize a Binomial random variable

## Inferences

- Define confidence interval
- Define confidence level for a confidence interval
- Calculate a confidence interval for a mean with a large sample size
- Effect on a confidence interval of increasing the sample size
- Effect on a confidence interval of increasing the confidence level
- Calculate a confidence interval for a mean with a small sample size
- Calculate a confidence interval for the Bernoulli parameter
- Define null hypothesis
- Define test statistic in the context of hypothesis testing
- Define critical value in the context of hypothesis testing
- Interpret the meaning of significance at level alpha
- Define p - value
- Distinguish Type I errors from Type II errors
- Identify when one-tailed vs. two-tailed tests should be used
- Define control group in the context of testing
- Describe randomization in the context of testing
- Describe blocking in the context of testing
- Define placebo effect in the context of testing
- Describe double blind testing
- Calculate p-value
- Calculate the power of a test against an alternative hypothesis

## Paired Data

- Distinguish data exhibiting positive negative and zero covariance
- Calculate covariance
- Explain the difference between covariance and correlation
- Distinguish strong weak and negligible correlation values
- Calculate correlation
- Calculate the mean of a sum of two random variables
- Calculate the standard deviation of a sum of two random variables
- Distinguish independent and dependent vars in a regression model
- Transform non-linear data into linear data for a regression
- Use a simple regression model for prediction
- Use a simple regression to predict impact of changes to independent variable
- Distinguish between small and large R
^{2}values in plotted data - Interpret the R
^{2}value in a regression model - Use a multiple regression model for prediction
- Use a multiple regression to predict impact of changes to independent variables
- Interpret the coefficient for the dummy variable
- Determine a confidence interval for a regression coefficient
- Determine the p-value for a regression coefficient
- Explain how the confidence in predictions of a multiple regression model can be improved