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Quantitative Methods

QMS 202

Clare Chua- Chow

Winter

Description

Confidence Interval: (INTR) – The true difference in means falls inbetween the confidence interval
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.
2-Prop Z Interval - calculates the confidence interval for the difference between the proportion of successes in two populations.
2-Sample t Interval - calculates the confidence interval for the difference between two population means when both population standard
deviations are unknown.
2-Sample Z TEST: 2-Propotion Z TEST: 2-Sample t TEST:
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 be left sx1:
NOTE: the intervals can be turned around so and they could both be positives even if it NOTE: the intervals can be turned around
left could be right and right could be left and shows a negative make sure to put it into so left could be right and right could be left
they could both be positives even if it shows a to question and see it makes sense and they could both be positives even if it
negative make sure to put it into to question shows a negative make sure to put it into
and see it makes sense to question and see it makes sense
α = significance level
Critical Value: (DIST) – STAT value ----------------- Critical Z value = Stat – Dist – Norm – InvN ------ Z value = + and -
DIST – NORM – InvN DIST – t – Invt
Tail: right, left , centre Area: 1 – level of significance for right or left tail test AND for two tail
Area: percentage test 1 – level of significance/2
σ: standard deviation = 1 df: n – 1 (n = sample size)
µ: = 0 ANSWER = – but the + and – of the answers is the non-rejection
region between them and outside is the 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)
2-Sample Z Test - tests the equality of the means of two populations based on independent samples when both population standard deviations
are known.
2-Prop Z Test - tests to compare the proportion of successes from two populations.
2-Sample t Test - compares the population means when the population standard deviations are unknown.
H0: µ or π = ≥ ≤
Ha: µ or π ≠ < >
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), <
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
1. Freq1: 1 F-Test: For testing the equality of two Z Stat = x(with mark on top) - µ ÷ (σ ÷ n Freq2: 1
variances – this tes

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