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Lecture

# Lecture 2

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Ryerson University

Quantitative Methods

QMS 202

Clare Chua

Winter

Description

1/17/2011
Objective
Learn how to coonnssttrrucctt and
Chapter 9
intteerrprreett confidence interval
Confidence Interval Estimation esttmamatess
Confidence Interval Estimation for the Mean ( known) For the mean
Confidence Interval Estimation for the Mean ( unknown) For the proportion
Confidence Interval Estimation for the Proportion
Determining Sample Size
Frequently asked questions
Confidence Interval
Estimation
1. is known and is unknown
is given and is not given
Population Mean 2 Population Proportion - 2. What is Z scores/values?
X Normal and/or nJ30? np J 5 and n(1-p) J 5? Go to this link to understand "z-score" :
If no stop. If no stop. http://www.youtube.com/watch?v=1xhCL5m4nI0&feature=
BF&list=QL&index=1
8 known? 8 unknown? http://www.youtube.com/watch?v=s0lLBcARxL4&feature=
Limits: p(1
p) mfu_in_order&list=UL
p H z n Cut and paste the link on the URL box.
p=x/n
x H z 3. What are you estimating? Parameters 2 or 5
Limits: n Limitsx H t 4. How do you interpret CI?
df=n-1 n
Go to this link
http://www.youtube.com/watch?v=hP6flJdoIxc&feature=f
WE EEEK 11 WEEEEKK 2 vw
Review 8
% Confidence Interval when is xivHnz:, / 2
=2 n
We needed z value for a % confidence Interval.
90% confidence leveConfidence coefficient of 0.90???
95% confidence leveConfidence coefficient oZ= ??????
97% confidence leveConfidence coefficient oZ= ??????
99% confidence leveConfidence coefficient oZ= ??????
% Confdence IIntterhen iis nott giiven : s
x H t , ,n
1
We needed t value for a % confidence Interval.n
H3 H2 H1 +1 +2 +3 Suppose we needed to find t, when sample size (denoted as n) is 25.
1 3 5 7 9 11 13 Xscale(=7, =2)
H3 H2 H1 0 +1 +2 +3 Zscale(=0, =1) 90% confidence levConfidence coefficient ot = ??????
Convert any normal random variable X to standardized normal 95% confidence levConfidence coefficient ot = ??????
random varX
2 Z. 97% confidence levConfidence coefficient ot = ??????
Z 8 99% confidence level
If X is normally distributed N(, ), the standardized variable Z has Confidence coefficient ot = ??????
standard deviation 1 (or =1), denoted N(0,1)r =0) and
1
www.notesolution.com 1/17/2011
TEMPLATE : : Confidence Interval for population mean TEMPLATE :: Confidence Interval for population mean
when is known when is unknown
Define : Estimate Define : Estimate
95% CI : s
95% CI : x H t. ,n
1
x H Z . 2 n Note:
2 n Confidence intervalto find the
Note: 1. Using the table to find t value and
1.8 Theearehre wayyo ndheth 33 use he fformuld heCII.fiind
20 .0 H 1.9566 Confidence interval 22555 .0 H 22.006440
50 1. Use the formula, find z value 25 2. Using the formula, find t value
ufrom CASIO calculatorn using SPSS function:
2. Use the formula, find z value 255 .0 H 13 .6 IDF.T (./2, degree of freedom)
20 .0 H 0.5 using SPSS function: compute function. using SPSS
IDF.Normal (prob, mean, stdev) 3. Using the INTR function of CASIO
3. Use the INTR function of CASIO 241 .3 @ @ 268 .6 Calculator to find Confidence
Calculator to find Confidence Interval directly
19 .5 @ @ 20 .5 Interval directly
Confidence Interval
Estimation Interpreting the CI
Population Mean 2 Population Proportion -
Read page 369, .with 95%
X Normal and/or nJ30? np J 5 and n(1-p) J 5?
If no stop. If no stop. confidence, you conclude that the
mean amount of all the sales
8 known? 8 unknown? iinvoiices ibei ttweenLII(llower
Limits: interval) and UI (upper interval).
p H z(1
p)
p=x/n n
Limits:H z n Limitx H t
df=n-1 n Referring to population
WEEEEK 11 WEEEEKK 2
Confidence Interval Estimation for
the proportion
The unknown population proportion is
represented by 5
Confidence Interval Estimation
The point estimate for 5 is the sample
for the p propportion
prropoortion, deenotedd as p, whhere p==X/nn
Where n = sample size (number of observed items/subjects in a sample)
We extends the concept of CI to categorical data And X=number of items in the sample having the characteristic of interest
Here you are concerned with estimating the proportion of
items in a population having a certain characteristic of
interest (e.g. people who have an iphone)
2
www.notesolution.com 1/17/2011
TEMPLATE : Confidence Interval for population
proportion, - Note
Define : est - = population proportion of __________________
State the n and p values p(1
p)
p H z
Check the conditions: np > 5 and n(1-p) > 5 n
If conditions are satisfied, proceed to find CI

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