Study list for exam 3

The R functions we have discussed in these weeks:

qt()

t.test()

pchisq()

chisq.test()

lm()

augment()

Lecture 15 Confidence Intervals

Distribution of proportion estimate
Confidence Intervals for Proportions
SRS Assumption
CI manipulations
Confidence Interval for Mean
t-distributions
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