# 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