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# QMS 202 Final: QMS 202 crib sheet Final Exam

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Ryerson University

Quantitative Methods

QMS 202

Clare Chua- Chow

Winter

Description

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: 2-Sample Z Interval:
C-Level: Confidence Interval C –Level : Confidence Interval
σ: Standard Deviation x with dash on top: mean
x with dash on top : mean sx: standard deviation
n: sample size 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 = significance level
1 – Confidence interval % = α
2-Sample Z Interval: 2-Propotion Z Interval: 2-Sample t Interval:
C-Level: Confidence Interval = 1 – α C-Level: Confidence Interval = 1 – α LIST MODE:
σ1: standard deviation of sample 1 x1: mean of sample 1 P1: =,
σ2: standard deviation of sample 2 N1: sample size of 1 List1: List 1
x1: mean of sample 1 x2: mean of sample 2 List2: List 2
N1: sample size of 1 N2: sample size of 2 Freq1: 1
x2: mean of sample 2 ANSWER: Freq2: 1
N2: sample size of 2 Left: Left end of interval Pooled: Off
ANSWER: Right: Right end of Interval ANSWER:
Left: Left end of interval P1(with roof): point estimate of proportion Left: Left end of interval
Right: Right end of Interval P2(with roof): point estimate of proportion Right: Right end of Interval
P1(with roof): point estimate of proportion N1: Sample size 1 df: degree of freedom
P2(with roof): point estimate of proportion N2: Sample size 2 x1: mean of sample 1
N1: Sample size 1 NOTE: the intervals can be turned around x2: mean of sample 2
N2: Sample size 2 so left could be right and right could sx1: standard deviation
NOTE: the intervals can be turned around so be left and they could both be NOTE: the intervals can be turned around
left could be right and right could be left positives even if it shows a negative so left could be right and right could
and they could both be positives even if it make sure to put it into to question be left and they could both be
shows a negative make sure to put it into to and see it makes sense positives even if it shows a negative
question and see it makes sense 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 DIST – CHI - InvC
Tail: right, left , centre Area: 1 – level of significance for right or Area = α/2 for two tail test and α Area:
left tail test AND for two tail test 1 – for one tail test
Area: percentage level of significance/2 df: n-1
df: n – 1 (n = sample size) N:df=numerator degree of
σ: standard deviation = 1 freedom – N1-1
ANSWER = – but the + and – of the
µ: = 0 answers is the non rejection region D:df=denominator degree of
between them and outside is the freedom– N2-1
rejection region
𝑧_𝑠𝑐𝑜𝑟𝑒 = (𝑥−μ)÷𝜎 ----------- x = claim value, μ = population mean ,𝜎 = 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 = + 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 1-Sample:
µ0: claim value µ0: claim value
σ: standard deviation x with dash on top: mean
x with dash on top: mean sx: standard deviation
n: sample size 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 value is larger than α Do not reject H0
If p value is less than α reject H0
2-Sample Z TEST: 2 indep POP σ known 2-Proportion Z Test: 2-Sample t Test: 2 indep POP σ equal but
µ1: =, >, < P1: =, unknown, 2 indep POP σ unequal and
σ1: standard deviation of sample 1 x1: mean of sample 1 unknown, 2 dep POP σ equal but unknown
σ2: standard deviation of sample 2 N1: sample size of 1 -Normally distributed with the same variance
x1: mean of sample 1 x2: mean of sample 2 -normally distributed with unequal variance
N1: sample size of 1 N2: sample size of 2 µ1: =, >(higher/greater), < (lower/less)
x2: mean of sample 2 ANSWERS: x1: mean of sample 1
N2: sample size of 2 P1: alternative hypothesis SX1: Standard deviation of sample 1
ANSWERS: Z: Z test statistic N1: sample size of 1
µ1: alternative hypothesis P: p value x2: mean of sample 2
z: z test statistic P1(with roof): sample proportion SX2: Standard deviation of sample 2
p: p value P2(with roof): sample proportion N2: sample size of 2
x1: mean of sample 1 P(with roof): pool propotion Pooled: ON
x2: mean of sample 2 LIST MODE:
N1: sample size of 1 Since p value is less than P1: =,
N2: sample size of 2 -If p value is larger than α Do not reject H0 List1: List 1
____________________________________ -If p value is less than α reject H0 List2: List 2
F-Test: For testing the equality of two Freq1: 1
variances – this test is done instead of Z Stat = x(with mark on

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