One sample T-test

one mean, mu and variance are unknown

1. State the hypothesis:

a. H0: vs Ha:

2. let

3. t-test:

4. set your rejection region. tobs| # < t* we do not reject the H0

5. Threshold approach:

a. |tobs| # < t* we do not reject the null hypothesis. That is there

is no significant evidence to suggest the mean “ “ is different

from “ “

6. 95% CI :

one sample t-test assumptions:

- observations are independent and identically distributed (iid)

and randomly sampled

- the mean (

is to be normally distributed (n 25)

o N(

Two-sample with equal variance

2 independent means

- welch, vs pooled

- assume

- is there actually a difference?

1. H0: vs Ha:

2. Let =0.05

3. t-test:

a. (pooled)

4. Rejection:|tobs| # < t* we do not reject the null hypothesis….

5. |tobs| # < t* we do not reject the null hypothesis. That is there is no

significant evidence to suggest the mean “ “ is different from “ “

6. 95% CI for 2 sided:

)

Paired t-test

given a difference chart, 2 populations, NOT independent (dependent)

1. H0: vs Ha:

2. Let =0.05

3. T-test:

4. Rejection region.

5. |tobs| # < t* we do not reject the null hypothesis. That is there is no

significant evidence to suggest the mean “ “ is different from “ “

6. 95% CI :

- The paired t-test removes variability and therefore decreases some

potential confounding variables, essentially leading to heightened

accuracy

- Uses 2 populations that are DEPENDENT of each other

2-sample t-test assumptions:

- Observations are independent

- Observations in each population are normally distributed if sample

sizes are small

- Equal variance among 2 populations

Welch T

unequal variances, how different are the samples?

1. SEw(

=

2. Df=

3. Tobs=

4. 95% CI:

Errors:

Type 1: reject the H0 when it is true

p-value is very small (<0.05

type 2: fail to reject the null when null is false p-value is

large (>0.05)

95% CI interpretation: We are 95% confidence that the true

difference of the 2 means is between ( , ). Because the CI

covers zero, there is a lack of evidence to suggest a

difference between ….. thus, suggesting there is no

difference in means

sample variance=

sample SD

95% CI will ALWAYS be 0.975

one sided tobs : 1-

two sided |tobs|: 1-

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