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Final

QMS 202 Study Guide - Final Guide: Simple Linear Regression, Null Hypothesis, Railways Act 1921


Department
Quantitative Methods
Course Code
QMS 202
Professor
Clare Chua- Chow
Study Guide
Final

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Confidence Interval: (INTR) The true difference in means falls in-between the confidence interval
1-Sample Z Interval - calculates the confidence interval for an unknown population mean when the population standard deviation is known.
2-Sample Z Interval - calculates the confidence interval for the difference between two population means when the population standard
deviations of two samples are known.
1-Prop Z Interval - calculates the confidence interval for an unknown proportion of successes.
2-Prop Z Interval - calculates the confidence interval for the difference between the proportion of successes in two populations.
1-Sample t Interval - calculates the confidence interval for an unknown population mean when the population standard deviation Is unknown.
2-Sample t Interval - calculates the confidence interval for the difference between two population means when both population standard
deviations are unknown.
INTR - Z Interval
INTR - t Interval
1-Sample Z Interval:
C-Level: Confidence Interval
σ: Standard Deviation
x with dash on top : mean
n: sample size
2-Sample Z Interval:
C Level : Confidence Interval
x with dash on top: mean
sx: standard deviation
n: sample size
1-Proportion Z Interval:
C-Level: Confidence interval
X: # of success
n: sample size
left = left side of interval
right = right side of interval
p with mark on top = centre of interval, sample proportion
α = sigifiae leel
1 Cofidee iteal % = α
2-Sample Z Interval:
C-Level: Confidence Interval = 1 α
σ: stadad deiatio of sample 1
σ: stadad deiatio of saple 
x1: mean of sample 1
N1: sample size of 1
x2: mean of sample 2
N2: sample size of 2
ANSWER:
Left: Left end of interval
Right: Right end of Interval
P1(with roof): point estimate of proportion
P2(with roof): point estimate of proportion
N1: Sample size 1
N2: Sample size 2
NOTE: the intervals can be turned around so
left could be right and right could be left
and they could both be positives even if it
shows a negative make sure to put it into to
question and see it makes sense
2-Propotion Z Interval:
C-Level: Confidence Interval = 1 α
x1: mean of sample 1
N1: sample size of 1
x2: mean of sample 2
N2: sample size of 2
ANSWER:
Left: Left end of interval
Right: Right end of Interval
P1(with roof): point estimate of proportion
P2(with roof): point estimate of proportion
N1: Sample size 1
N2: Sample size 2
NOTE: the intervals can be turned around
so left could be right and right could
be left and they could both be
positives even if it shows a negative
make sure to put it into to question
and see it makes sense
2-Sample t Interval:
LIST MODE:
P1: =, <, >
List1: List 1
List2: List 2
Freq1: 1
Freq2: 1
Pooled: Off
ANSWER:
Left: Left end of interval
Right: Right end of Interval
df: degree of freedom
x1: mean of sample 1
x2: mean of sample 2
sx1: standard deviation
NOTE: the intervals can be turned around
so left could be right and right could
be left and they could both be
positives even if it shows a negative
make sure to put it into to question
and see it makes sense
Critical Value: (DIST) STAT value ----------------- Critical Z value = Stat Dist Norm InvN ------ Z value = + and -
DIST NORM InvN
DIST t Invt
DIST F - InvF
Tail: right, left , centre
Area: percentage
σ: standard deviation = 1
µ: = 0
Area: 1 level of significance for right or
left tail test AND for two tail test 1
level of significance/2
df: n 1 (n = sample size)
ANSWER = but the + and of the
answers is the non rejection region
between them and outside is the
rejection region
Area = α/ for two tail test and α
for one tail test
N:df=numerator degree of
freedom N1-1
D:df=denominator degree of
freedom N2-1
_ = (μ)÷ ----------- x = claim value, μ = population mean , = Standard deviation
**If you need to find x find z score using InvN and plug the answer into the z score equation
** For a two tailed test answer = + and - OR for one tail left = - OR for one tail right = +
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Hypothesis Testing: (TEST)
H0: µ or π
=
Ha: µ or π
<
>
TEST - Z
TEST - t
1-Sample: Convert x with mark on top to Z stat
µ0: claim value
σ: standard deviation
x with dash on top: mean
n: sample size
1-Sample:
µ0: claim value
x with dash on top: mean
sx: standard deviation
n: sample size
1-Proportion:
P0: Claim value
x: # of success
n: Sample Size
Answers:
z = z test
p = p-value
p with mark on top = sample proportion
If p alue is lage tha α Do ot ejet H
If p alue is less tha α reject H0
2-Sample Z TEST:  idep POP σ ko
µ1: =, >, <
σ: stadad deiatio of saple 
σ: stadad deiatio of saple 
x1: mean of sample 1
N1: sample size of 1
x2: mean of sample 2
N2: sample size of 2
ANSWERS:
µ1: alternative hypothesis
z: z test statistic
p: p value
x1: mean of sample 1
x2: mean of sample 2
N1: sample size of 1
N2: sample size of 2
____________________________________
F-Test: For testing the equality of two
variances this test is done instead of
assuming that variances are equal
σ and degrees of freedom
n1-1= degrees of freedom from sample 1
(i.e. the numerator degrees of freedom)
n2-1= degrees of freedom from sample 2
(i.e. the denominator degrees of freedom)
Note: The test statistics F follows an F
distribution with n1-1 and n2-1
F= variance of sample 1/ variance of sample 2
2-Sample F Test
µ1: =, >, <
SX1: Standard deviation of sample 1
N1: sample size of 1
SX2: Standard deviation of sample 2
N2: sample size of 2
ANSWERS:
F = F statistic
P = p value
Fstat > critical value do not reject
insufficient evidence
Fstat < Critical value = reject ho sufficient
evidence
2-Proportion Z Test:
P1: =, <, >
x1: mean of sample 1
N1: sample size of 1
x2: mean of sample 2
N2: sample size of 2
ANSWERS:
P1: alternative hypothesis
Z: Z test statistic
P: p value
P1(with roof): sample proportion
P2(with roof): sample proportion
P(with roof): pool propotion
Since p value is less than
-If p alue is lage tha α Do ot ejet H
-If p alue is less tha α ejet H
Z Stat = x(with mark on top) - µ ÷ (σ ÷ n
squared)
Z Stat greater than z critical value do not
reject H0
Z Stat less than z critical value reject H0
-The P value, or calculated probability, is
the probability of finding the observed, or
more extreme, results when the null
hypothesis (H 0) is true
2-Sample t Test:  idep POP σ equal but
uko,  idep POP σ unequal and
uko,  dep POP σ eual ut uko
-Normally distributed with the same variance
-normally distributed with unequal variance
µ1: =, >(higher/greater), < (lower/less)
x1: mean of sample 1
SX1: Standard deviation of sample 1
N1: sample size of 1
x2: mean of sample 2
SX2: Standard deviation of sample 2
N2: sample size of 2
Pooled: ON
LIST MODE:
P1: =, <, >
List1: List 1
List2: List 2
Freq1: 1
Freq2: 1
Pooled: Off
ANSWERS:
µ1: alternative hypothesis
t: test statistic
p: p value
df: degree of freedom
x1: mean of sample 1
x2: mean of sample 2
sx1:
sx2:
n1: sample size 1
n2: sample size 2
-dependent sample paired t-test
First find t critical value
Create a table by subtracting table a b
Use 1 sample t test
Mo:0
List:List 1
Freq:1
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