Study Guides (283,485)
CA (135,432)
U of G (7,473)
STAT (72)
STAT 2050 (6)
Zeny Feng (6)
Midterm

STAT 2050 Midterm: test 1 stats sheet

1 Page
27 Views
Spring 2018

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

This preview shows half of the first page. Sign up to view the full page of the document.
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-
find more resources at oneclass.com
find more resources at oneclass.com

Loved by over 2.2 million students

Over 90% improved by at least one letter grade.

Leah — University of Toronto

OneClass has been such a huge help in my studies at UofT especially since I am a transfer student. OneClass is the study buddy I never had before and definitely gives me the extra push to get from a B to an A!

Leah — University of Toronto
Saarim — University of Michigan

Balancing social life With academics can be difficult, that is why I'm so glad that OneClass is out there where I can find the top notes for all of my classes. Now I can be the all-star student I want to be.

Saarim — University of Michigan
Jenna — University of Wisconsin

As a college student living on a college budget, I love how easy it is to earn gift cards just by submitting my notes.

Jenna — University of Wisconsin
Anne — University of California

OneClass has allowed me to catch up with my most difficult course! #lifesaver

Anne — University of California
Description
One sample Ttest Welch T one mean, mu and variance are unknown unequal variances, how different are the samples? 1. State the hypothesis: 2 2 1 2 a. H 0 1= v2 H : a= 1 2 1. SE (w 1 )= 2 1+ 2 2. let = 0.05 2 2 ( 1+ 2 ) 3. ttes t: = = 1 2 () 2. Df= 22 2 1 ( 1 )+ 1 ( 2 ) ~ 1 11 1 21 2 1 2 0 4. set your rejection regioobs < t* we do not reject th0 H 3. T =obs 2 5. Threshold approach: 1 + 2 a. tobs < t* we do not reject the null hypothesis. That is there 1 2 is no significant evidence to suggest the mean is different + 4. 95 CI: 1 2 ,0.975 1 ) 2 from 6. 95 CI : + () Errors: 0.975, Type 1: reject the 0 when it is true one sample ttest assumptions: pvalue is very small (<0.05 observations are independent and identically distributed (iid) type 2: fail to reject the null when null is false pvalue is and randomly sampled large (>0.05) the mean () is to be normally distributed (n 25) o N(, ) ~ 0 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 Twosample with equal variance 2 independent means difference between .. thus, suggesting there is no difference in means welch, vs pooled assume 1 =2 3 is there actually a difference? 2 ( ) 2 sample variance= = =1 1 1. H :0 1 = 2 vs H : a 1 0 2 ()2 2. Let =0.05 sample SD = = 2 =1 1 12 3. ttest: = (1 2 95 CI will ALWAYS be 0.975 1 2 ~ one sided tobs: 1> 2 > 1 1 1 1 1+ 22 two sided t : = = 0 1 1+ 2 obs 1 2 1 2 ( 1 +( 1) 2 a. (pooled) = 1 1 2 2 1 21 4. Rejection:obs < t* we do not reject the null hypothesis. 5. obs < 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: ( 1 + 1 ) 1 2 0.975, 1 2 Paired ttest given a difference chart, 2 populations, NOT independent (dependent) 1. H :0 = 0 vs H : a 0 2. Let =0.05 0 3. Ttest : = ~ 1 0 ( ) 4. Rejection region. 5. obs < 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 : 0.975,() The paired ttest removes variability and therefore decreases some potential confounding variables, essentially leading to heightened accuracy Uses 2 populations that are DEPENDENT of each other 2sample ttest assumptions: Observations are independent Observations in each population are normally distributed if sample sizes are small Equal variance among 2 populations
More Less
Unlock Document

Only half of the first page are available for preview. Some parts have been intentionally blurred.

Unlock Document
You're Reading a Preview

Unlock to view full version

Unlock Document

You've reached the limit of 4 previews this month

Create an account for unlimited previews.

Already have an account?

Log In


OR

Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit