Ch. 18 - Sampling Distributions

18.1: Understand and interpret sampling distributions of means and proportions
  1. Understand that the variability of a statistic(as measured by standard deviation of its sampling distribution) depends on the size of the sample.
  2. Be able to demonstrate a sampling distribution by simulation
  3. Be able to use a sampling distribution model to make simple statements about the distribution of a proportion or mean under repeated sampling
  4. Be able to interpret a sampling distribution model as describing the values taken by a statistic in all possible realizations of a sample or randomized experiment under the same conditions
  5. Statistics based on larger samples are less variable
18.2: Understand and explain the Central Limit Theorem
  1. Understand that the CLT gives the sampling distribution model of the mean for sufficiently large samples regardless of the underlying population

Ch. 20 - Testing Hypotheses About One Proportion

20.1 - Be able to state the null and alternative hypotheses for a one-proportion z-test
  1. Be able to identify and use the alternative hypothesis when testing hypotheses
  2. Understand how to choose between a one-sided and two-sided alternative hypothesis and be able to explain your choice
  3. Know how to defend the choice of a one-sided alternative
20.2 - Know the conditions that must be true for a one-proportion z-test to be appropriate
  1. Know how to examine your data for violations of these conditions
20.3 - Be able to perform a one-proportion z-test
20.4 - Know how to interpret the meaning of a P-value in nontechnical language
  1. Make clear that the probability claim is made about computed values under the assumption that the null model is true and not about the population parameter of interest
  2. Understand that the P-value of a test does not give the probability that the null hypothesis is correct
20.5 - Be able to make a conclusion based upon results of a one-proportion z-test
  1. Know that we do not "accept" a null hypothesis if we cannot reject it, bur rather we can only "fail to reject" the hypothesis for lack of evidence against it

Ch. 19 - Confidence Intervals for Proportions

19.1 - Be able to construct a one-proportion z-interval
19.2 - Be able to interpret a one-proportion z-interval in a simple sentence or two.
  1. Understand confidence intervals as a balance between the precision and the certainty of a statement about a model parameter
  2. Understand that the margin of error of a confidence interval for a proportion changes with the sample size and the level of confidence
  3. Write such an interpretation so that it does not state or suggest that the parameter of interest is itself random, but rather that the bounds of the confidence interval are the random quantities about which we state our degree of confidence.

Ch. 22 - Inference for Two Proportions

22.1 - Be able to state a null and alternative hypothesis for testing the difference between two population proportions
22.2 - Know the conditions that must be true for a two-proportion z-test to be appropriate
22.3 - Know how to find and interpret a confidence interval for the difference between two proportions
  1. Be able to write a sentence describing what is said about the difference between two population proportions by a confidence interval
22.4 - Be able to perform a significance test of the natural null hypothesis that two population proportions are equal
  1. Know how to write a sentence interpreting the results of a significance test of the null hypothesis that two population proportions are equal

Ch. 21 - Errors and Power
21.1 - Be able to explain statistical significance21.2 - Understand the relationship between hypothesis tests and confidence intervals21.3 - Understand and be able to explain alpha, alpha levels, and type I errors21.4 - Understand and be able to explain beta and type II errors21.5 - Understand and be able to explain the power of a test