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Midterm

STAT 2050 Study Guide - Midterm Guide: Independent And Identically Distributed Random Variables, Null Hypothesis

1 pages53 viewsSpring 2018

Department
Statistics
Course Code
STAT 2050
Professor
Zeny Feng
Study Guide
Midterm

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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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