Study list for exam 3

The R functions we have discussed in these weeks:


Lecture 15 Confidence Intervals

Distribution of proportion estimate
Confidence Intervals for Proportions
SRS Assumption
CI manipulations
Confidence Interval for Mean
Margin of Error
SRS condition and Sample size condition

Lecture 16 Statistical Tests

Null and alternative hypotheses
Type I and II Errors for Tests Testing a proportion: \[ \hat p\sim \mathcal{N}\left(p_0, \frac{p_0(1-p_0)}{n}\right)\] Multiple testing, impact and motivation

Lecture 17 Comparison

Two sample z-test for proportions
Standard Error formula
Assumptions for two-sample z-test for proportions
Confidence Interval for Difference between Means
\[(\bar X_1 - X_2 - t_{\alpha/2}\text{se}(\bar X_1-\bar X_2),\bar X_1 - X_2 + t_{\alpha/2}\text{se}(\bar X_1-\bar X_2))\]

\[\text{se}(\bar X_1-\bar X_2) = \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}.\]

Code for paired t-test in R

Paired comparisons

Lecture 18 Inference for Counts

Testing for independence using \(\chi^2\) test
Testing for goodness of fit using \(\chi^2\) test
Degrees of freedom: \[\text{df}=(r-1)(c-1)\]
R code to perform \(\chi^2\) test and get p-value from test statistic

Lecture 19 Linear Patterns

Response and explanatory variables
\(R^2\) for linear models
Slope and intercept for linear models
Mathematical formulas for slope and intercept
Residuals of linear model
R code for fitting linear models