Inference from normal distribution Flashcards
One sampled T test
A one-sample t-test compares the sample mean with a specific value for the population mean proposed in a null hypothesis.
Under the null hypothesis that the population mean is equal to μ0, the sampling distribution of the test statistic t=y-u0/ SEY is a t-distribution with n−1degrees of freedom.
1) Work out SEY bar= sample standard deviation / sqrt population size
unlike with Z standardisation you are using sample standard deviation rather than population standard deviation to calculate standard error.
This value depends on the sample size (degree of freedom).
2) Work out the T statistic
t=y-u0/ SEY
If the population mean and the sample mean are equal then the T statstic is 0. The T statistic shows how many standard deviations the sample mean is from the population mean.
3) You work out the P value from the T table
Similair to Z standardization but Z standardization requires the population sd which is often unknown. For OS T-test you use sample SD to work out sample SE.
The confidence interval for a mean of a normally disitrbuted population
The T disitrbution can be used to find the confidence interval for a population that is normally disitributed.
Y-t0.05(2),df x SEY < u < Y+t0.05(2),df x SEY
Assumptions of 1 sampled T test
1) The data are a random sample from a population
2) The variability is normally distributed in the population
(Note: the t‐test is robust to minor violations of the normality assumption.
Z disitrbution vs T distribution
SEY-bar (SE using sample sd) is not constant like σY-bar (SE using population sd) because s varies from sample to sample so t-distribution not the same as normal distribution (=wider distrib w/ fatter tails than standard normal distribution).
As sample size increases, t becomes more like Z.
