Slides 20 ⊹₊ ⋆ Flashcards
What are the main topics covered in Test 2?
Confidence Intervals for means and proportions, Hypothesis Testing, Sample Proportion, 1-sample t test, Unpaired/paired 2 sample t test, ANOVA, Basics of linear regression, Visually analyzing data, Constructing a Model, Interpreting R output, Any scientific paper using any of these methods.
Which topics are omitted from Test 2?
Omitted Variable Bias, Residual Analysis, Multivariable Models, Nonlinear Models, Interaction Terms, Multicollinearity.
What is the formula for a sample proportion confidence interval?
p̂ ± z*√((p̂(1-p̂)/n)
What are the null and alternative hypotheses for a sample proportion test?
H0: p = [value], HA: p ≠/>/< [value]
What are the conditions for the Central Limit Theorem (CLT) in hypothesis testing?
np ≥ 10, n(1-p) ≥ 10
What is the test statistic formula for a sample proportion?
z = (p̂ - p) / SE
What is the formula for a sample mean confidence interval?
x̄ ± t*s/√n
What are the null and alternative hypotheses for a sample mean test?
H0: μ = [value], HA: μ ≠/>/< [value]
What is the condition for sample size in a t-test?
n ≥ 30; if n < 30, data must look REALLY normal
What is the formula for the t statistic in a sample mean test?
t = (x̄ - μ) / SE
How do you find the p-value for a t-test?
pt(t, df=n-1)
What is the difference between paired and unpaired sample means?
Paired means use x̄diff, while unpaired means use (x̄A - x̄B)
What is the formula for the t statistic in an unpaired means test?
t = ((x̄A - x̄B) - (μA - μB)) / SE
What are the null and alternative hypotheses for an ANOVA test?
H0: no difference among means, HA: some difference among means
What conditions must be met for ANOVA?
Each group must pass t test conditions, variances should be roughly equal
What is the formula for the F statistic in ANOVA?
F = MSG/MSE
What is the definition of a confidence interval (CI)?
A range of values that is likely to contain the population parameter with a specified level of confidence.
What does z* represent in the context of confidence intervals?
The number of standard deviations away from the mean needed to capture the desired proportion of data.
For a 95% confidence interval, what is the value of z*?
1.96
For a 99% confidence interval, what is the value of z*?
2.58
What is the formula to calculate t* for a confidence interval?
qt(0.995, df=n-1)
What is the significance of the degrees of freedom in t-distribution?
Degrees of freedom adjust the t distribution based on sample size.
What statistical tests are covered in the examples provided?
Sample proportion, Sample mean, Paired sample means, Unpaired sample means, ANOVA, Regressions.
