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