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Chem 212!

Lecture 5!

Sept. 16/2016!

!

Graded assignment, identical question in class. Sometime next week!

Finish worksheets this weekend****!

!

Stats continued...!

-Stats test testing if there is a diﬀerence or not!

-at higher level conﬁdence we need much stronger evidence!

-Testing the null-hypothesis Ho!

#-xbar and mu are not signiﬁcantly diﬀerent and can be explained by random error alone!

#-testing whether the diﬀerence is real or not!

#-t value is the value expected only from only random error!

-Setting up the t-test!

#1. Calculate t-cal= |38.1-33.56|*(5^1/2/3.15)=3.2!

#2. Look up table: for d.f.=5-1!

#3. t-table=2.78 at 95% conf & t-table=4.60 at 99%!

#4. Conclude:!

##There is a signiﬁcant diﬀerence at 95%!

##There is not signiﬁcant at 99%!

!

The stronger evidence is saying there is something else going on rather than just random error.!

Your tcalc tells you if you can reject the null hypothesis that says there is no diﬀerence besides random error!

!

Steps for conducting a t-test:!

calc xbar and s!1.

Calculate talc!2.

look up t-table based on d.f. and desired level of conﬁdence!3.

compare talc and table!4.

make conclusion!5.

if t-calc>t-tbale there is a signiﬁcant diﬀerence at the selected conﬁdence interval!A.

t-calc<t-table there is not a signiﬁcant diﬀerence at the selected conﬁdence interval!B.

!

Comparison of means: Unpaired: xbar, s!

###########Secondary calculation!

######t-test EQN 1###S pooled!

-do an F test to choose !

!

######t-test EQN 2###degrees of freedom!

!

####do t-test!

#!

Comparisons of diﬀerences Paired:!

###don't average results!

!

###t-test on diﬀerences!

!

-dont expect the results to be the same therefore do not average them. Do our t-test on our diﬀerences!

!

-The hardest part of statistics for students is choosing paired or unpaired**!

Do not assume that whenever you have a list of numbers it is valid to average them!

-average only if the data points are replicate values for the same measurement!

!

Comparison of means t-test:

-must have unpaired data!

-ﬁrst use an F-test to select appropriate t-test and then do the t-test!

-F test compares s.d of one data set (Sa) to that of second data set (Sb)!

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