Confidence intervals & statistical testing

Question 1

Sampling distribution

Answer 1

Under random sampling, sample mean good estimate of population mean.
When sampled from Gaussian distribution, sample mean also has Gaussian distribution.

Question 2

Squared standard error of the mean

Answer 2

Variance of the sample mean

Question 3

Standard error of the mean

Answer 3

Square root of the sample variance

Question 4

Confidence interval

Answer 4

An interval (based on observed data) that contains an unknown population parameter with some specified probability.
Statement about the likelihood that true parameter value occurs between two bounds. 
NOT probability a value falls between 2 points.
NOT amount of certainty that an estimate takes a certain value.
NOT variability in an estimate.

Question 5

Critical value

Answer 5

Value of a distribution that occurs with a certain level of probability. 
Normal distribution:
-1 to 1 = 68% of density
-1.96 to 1.96 = 95% of density
-2.58 to 2.58 = 99% of density

Question 6

α

Answer 6

Probability of making a mistake.

P(-c

Question 7

t distribution

Answer 7

T = (Xbar - mu)/((s/SQRT(n))

Distribution only depends on size of sample or degrees of freedom (n-1).

Question 8

Two forms of error

Answer 8

Type 1 error: Reject the null when it’s in fact true. Probability is equal to alpha level.
Type 2 error: Fail to reject the null when it’s in fact false. Called beta, & speak in terms of power to reject the null when it is false (1-beta).

Question 9

Test for normality

Answer 9

Shapiro-Wilk test.
Compares the quantiles of your distribution to those of a normal distribution.
Generates a test statistic, W, & a p-value which tell us if data “normal” or not.

Question 10

Hypothesis testing

Answer 10

z-test for the mean, test a sample mean vs. a hypothesized mean value.

Question 11

p-values

Answer 11

p-values are probabilities.
Probability of seeing a test statistic as large ast he one we calculate, then test doesn’t negate null hypothesis.
If test statistics like ours occur very rarely, then have small p value & conclude support for research hypothesis.