Unformatted text preview: BIT 2405 Quantitative Methods I
BIT 2405 Quantitative Methods I
Test 3 Preparation
Chapters 9 & 11.1 This Week and Next.
This Week and Next.
Lectures Hawkes Today Optional HW911 and
Optional
Required Quiz 3
Required
due @ 9 am 11/19 NOW IS
NOW IS
THE TIME
THE TIME
tto ASK
o ASK
FOR
FOR
HELP!
HELP! Schedule Next Week.
Schedule Next Week.
Day
Monday
11/16
Tuesday
11/17 Content Time Help Session 11:00 am ROB105 Early Test 3 3:30 pm TORG2150 Wednesday
11/18
Thursday Test 3
11/19 11:00 am ROB105
3:30 pm TORG2150 Day
Monday
11/16
Tuesday
11/17 Schedule Next Week.
You MUST EMAIL ME by MONDAY You MUST EMAIL ME by MONDAY
Content @ 9AM and get Time
permission from me
9AM
to change your test from your
Scheduled Time.
Scheduled Help Session 11:00 am ROB105 Early Test 3 3:30 pm TORG2150 Your Scheduled Test Time IS on
Your
Wednesday
Thursday in the Time for which you are
11/18 ENROLLED.
ENROLLED. Thursday
11/19 Test 3 11:00 am ROB105
3:30 pm TORG2150 Questions?
Questions? Test 3
Test 3
s 25 Multiple Choice Questions • Covers Chapters 9 and 11.1
• Mostly “calculations” with looking up in Tables s 50 Minutes to Complete Chapter 9 Hypothesis Testing
9.1
9.2
9.3
9.4 Developing Null and Alternative Hypotheses Type I and Type II Errors Population Mean: σ Known
NOT ON
NOT Population Mean: σ Unknown
THE TEST
THE 9.5 Population Proportion Chapter 11
Chapter 11 Inferences About Population Variances
11.1 Inference about a Population Variance
11.2 Inferences about the Variances of Two Populations Interval Estimation:
Interval Estimation:
σ Only σ2 & σ
Only
2 ( n − 1) s2
( n − 1) s2
≤ σ2 ≤ 2
2
χ α /2
χ (1− α / 2) 1.
2.
3.
4. σ (n − 1) s 2
(n − 1) s 2
≤σ ≤
2
2
χα /2
χ (1−α / 2) Determine whether it’s variance or standard deviation
Calculate α/2 and the Degrees of Freedom, df = (n1)
Look up the two χ 2 values and Crunch the numbers. Hypothesis Testing
1. Three Basic Forms of the Null Hypothesis whether it’ s μ,
p, or σ.
(μ i s shown below) Determine the basic test required & SKETCH IT! H 0 : µ ≥ µ0 H 0 : µ ≤ µ0 H 0 : µ = µ0 Onetailed
(lowertail) Onetailed
(uppertail) Twotailed α α α/2 α/2 Hypothesis Testing
Hypothesis Testing
1.
2. Determine the basic test required & SKETCH IT!
Determine the Population Parameter of interest. μ p σ 2 Hypothesis Testing
Hypothesis Testing
1.
2. Determine what the basic test required & SKETCH IT!
Determine the Population Parameter of interest.
a. If μ, determine if σknown or σunknown p μ
σknown σunknown σ 2 Hypothesis Testing
Hypothesis Testing
1. Calculate the Test Statistic. p μ
σknown zobs = x − µ
σ/ n
0 σ 2 σunknown t obs = x − µ
s/ n
0 z obs = ˆ
p − p0 p0 (1 − p0 )
n χ 2
obs (n − 1) s 2
=
σ 02 Hypothesis Testing
Hypothesis Testing
1. “Reject” or “Do Not Reject” the Null Hypothesis using either the pvalue test OR critical value test
I ’ ll use the σknown case to illustrate.
I’ LowerTailed Test About a Population Mean:
σ Known
s pvalue Approach pValue < α ,
so reject H0. α = .10 Sampling
distribution of zobs = x − µ 3. Compare σ/ n pvalue
= .0 7 2
2. “ Look Up” pvalue
2. z z = 0 obs σ known 0 1.46 1. Calculate Zobs LowerTailed Test About a Population Mean:
σ Known
s Critical Value Approach Zobs < Zα ,
so reject H0. α = .10 Sampling
distribution of zobs = x − µ σ/ n 3. Compare Z’ s
2. Calculate Zobs z = obs σ known 1.46 0 z zα = 1.28 0
1. “ Look Up” Zα UpperTailed Test About a Population Mean:
σ Known
s pValue Approach Sampling
distribution of zobs = x − µ pValue <α ,
so reject H0. α = .04
0 σ/ n
pValue
= .0 1 1
z
0 σ known zα = 1.75 z =
obs 2.29 UpperTailed Test About a Population Mean:
σ Known
s Critical Value Approach Sampling
distribution of zobs = x − µ 0 σ/ n Reject H0 Do Not Reject H0
0 σ known α = .0 5 zα = 1.645 z TwoTailed Tests About a Population Mean:
TwoTailed Tests About a Population Mean:
σ Known pValue Approach 1/2
p value
= .0031 α = 0.03 α /2 = .015 α /2 = .015 z zα/2 = 2.17 0 zα/2 = 2.17 z = 2.74
obs TwoTailed Tests About a Population Mean:
σ Known Critical Value Approach Sampling
distribution of zobs = x − µ 0 σ/ n Reject H0 Reject H0 Do Not Reject H0 α/2 = .015 2.17 α/2 = .015
0 2.17 z Keep Track of What Population Parameter You Are Working With. p μ
σknown zobs = x − µ
σ/ n
0 ZTables σunknown t obs = x − µ
s/ n
0 TTables σ χ 2Tables ZTables
z obs = ˆ
p − p0 p0 (1 − p0 )
n 2 χ 2
obs (n − 1) s 2
=
σ 02 Keep Track of What Test Is Needed.
1. Determine the basic test required & SKETCH IT! H 0 : µ ≥ µ0 H 0 : µ ≤ µ0 H 0 : µ = µ0 Onetailed
Onetailed
(lowertail) Onetailed
(uppertail) Twotailed α α α/2 α/2 Keep Track of What You’re Looking Up. p μ
σknown
ZTables σunknown
TTables ZTables σ 2 χ 2Tables Keep Track of What You’re Looking Up. p μ
σknown
ZTables
• Symmetrical
Symmetrical
• Centered on 0
Centered
• Lower Tail Given
L ower σunknown ZTables σ 2 Keep Track of What You’re Looking Up. p μ
σknown •
•
•
•
• σunknown Symmetrical
Symmetrical
Centered on 0
Centered
Upper Tail Given
Upper
Degrees of Freedom
Degrees
Columns are Areas
Columns TTables σ 2 Keep Track of What You’re Looking Up. p μ
σknown σunknown • NOT Symmetrical
NOT
• NOT Centered on 0
NOT
•All Positive Values
• Upper Tail Given
Upper
• Degrees of Freedom
Degrees
• Columns are Areas
Columns σ 2 χ 2Tables Formula Sheet
Formula Sheet For the Test
For the Test
s
s s s VT Photo ID
Calculator • (Any calculator including graphing)
Pencils (#2)
NOT ALLOWED (Includes)
• Phone
• Computer
• Books, notes nor any other materials...
You will be given a FORMULA SHEET when you come to the Test.
You cannot use your own! Cheating and YOUR WORD.
Cheating and YOUR WORD.
The Rules
1. You must turn in all pages of the exam and the scantron form or you will receive a ZERO on this exam. 2. Make sure you correctly code in the test form and your Student ID on your scantron form. 3. You may not discuss this exam during the exam nor outside of this classroom until all of Dr. Jones's BIT2405 students have completed their exam. 4. You must pledge the exam or you will receive a zero. 5. The honor code is in effect for all exams. Pledge the exam to indicate you have neither given nor received help. This is a closed
book, closednotes exam. Sharing calculators is a violation of the honor code. Presence of a cell phone is a violation of the honor code. Cheating and YOUR WORD.
Cheating and YOUR WORD.
The Rules
I pledge that I have neither given nor received help on this exam. I will not discuss this exam with anyone in Dr. Jones’s BIT2405 classes until after all students have taken the exam. The last exams will be finished by 5 pm on
The
Thursday, November 19th.
Thursday, Cheating and YOUR WORD.
Cheating and YOUR WORD.
Close Quarters.
s Keep your SCANTRON FORM COVERED unless you are writing on it. s Keep your eyes on your own papers. s The GAs and I are VIGILANT about watching you and taking names of anyone suspected of cheating.
• I will follow the honor code to the fullest extent. s NO HATS ALLOWED! During the Test
During the Test
s I will not answer questions during the test!
• If you are missing a page or something like that, then please ask me. Otherwise, I don’t answer questions about the questions or the test in general. s I will not discuss the test with you after you finish.
• If you have a concern about a question on the test, please email me and I will address that the following week. s If you think none of the answers is correct, I suggest you RE
READ the PROBLEM to make sure you got the right Formula. Grades
Grades
s I will post grades in Scholar and email you when I’ve posted them.
• Hope to have this done at the latest by Monday, November 23rd. s I will NOT email your grade to you. DON’T FORGET…
DON’T FORGET…
s REQUIRED QUIZ 3 on Scholar goes away @ 9 am on Thursday, November 19th. s EMAIL me by Monday @ 9 am if you want to SWITCH TEST TIMES. Don’ t forget
Don’
your
CALCULATOR
CALCULATOR
! s BRING YOUR CALCULATOR to the Test. s Post Questions on the DISCUSSION BOARDS on BLACKBOARD if you need help beyond the sessions. Questions?
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This note was uploaded on 08/30/2011 for the course ART 3514 taught by Professor Dhbannan during the Summer '03 term at Virginia Tech.
 Summer '03
 DHBannan

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