(10) When to use each test

When is t-test/distribution used

Sample of n_x taken from normal dist with unknown σ² to test for μ

^t_n-1 dist where S² is an unbiased estimator of σ²

When is F-test used

Sample of n_x and n_y both taken from normal dist with unknown but equal σ²

EQUAL VARIANCE = F DIST

Confidence interval for population mean from small sample of normal distribution with unknown mean and variance

When to use paired t-test

Paired experiment with a mean of the differences between the samples of D bar

Pooled estimate for σ²

Top in formula book, not for s²_x or y

Confidence limits for the difference between the two means of 𝑋 and 𝑌:

Not in formula book

t_c = relevant value from t tables

Hypothesis test for difference between means of 2 Normal dists with known variance

Standardised normal/normal

(Use sample variance when population variance unknown for large n)

Confidence interval for population mean of normal dist

z = relevant % point from standardised normal

not in formula book

Width of confidence interval

2zσ/n^1/2

Confidence interval for variance of normal dist

α = probability variance falls outside limits (e.g. 90% interval, 10% confident outside range)

Hypothesis test and confidence interval for mean of normal dist with unknown variance