MAT 157 - Statistics

1. Analyze statistical processes. 
   1. Classify various sampling methods.
   2. Distinguish between data types.
   3. Identify the impact of experimental design on experimental results.
2. Create appropriate data representations.
   1. Construct tables, charts, and graphs.
   2. Interpret measures of center, position, and spread. 
3. Examine fundamentals of probability and counting.
   1. Utilize empirical and theoretical probability.
   2. Solve for the probability of simple, compound, conditional, independent, and mutually exclusive events.
   3. Choose appropriate counting principles.
4. Analyze probability distributions.
   1. Define a probability distribution in terms of a random variable.
   2. Examine discrete and continuous distributions.
   3. Identify the descriptive values for a given probability distribution.
5. Evaluate sampling distributions.
   1. Apply the Central Limit Theorem.
   2. Calculate the mean and standard error of a sampling distribution.
   3. Assess estimators in relation to sampling distributions.
6. Support statistical inference with confidence intervals.
   1. Determine confidence intervals for one and two sample scenarios.
   2. Interpret confidence intervals for one and two sample scenarios.
7. Create appropriate hypothesis test regarding one population parameter.
   1. Test claims about population proportions, means, and standard deviations.
   2. Evaluate claims about population proportions, means, and standard deviations using p-values.
   3. Discuss potential Type I and Type II errors of hypothesis tests.
   4. Support statistical inference by using confidence intervals.
8. Create appropriate hypothesis test regarding two population parameters. 
   1. Test claims about the difference of two independent means and proportions.
   2. Perform a matched pairs t-test.
   3. Assess claims about two population variances or standard deviations using the F-distribution.
   4. Use a chi-square distribution to conduct a goodness-of-fit test and test of independence.
   5. Support statistical inference by using confidence intervals.
9. Evaluate linear correlation and linear models.
   1. Determine and interpret the correlation coefficient and line of best fit.
   2. Test the correlation coefficient for significance.
   3. Generate the appropriate predicted values from the linear model.
   4. Analyze the residual plot to determine suitability of linear model.