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

by OC370112

School

Ryerson UniversityDepartment

Quantitative MethodsCourse Code

QMS 202Professor

Clare Chua- ChowStudy Guide

FinalThis

**preview**shows page 1. to view the full**5 pages of the document.**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 = sigifiae leel

1 – Cofidee iteal % = α

2-Sample Z Interval:

C-Level: Confidence Interval = 1 – α

σ: stadad deiatio of sample 1

σ: stadad deiatio of saple

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

DIST – CHI - InvC

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

Area:

df: n-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 lage tha α Do ot ejet H

If p alue is less tha α reject H0

2-Sample Z TEST: idep POP σ ko

µ1: =, >, <

σ: stadad deiatio of saple

σ: stadad deiatio of saple

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 lage tha α Do ot ejet H

-If p alue is less tha α ejet 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: idep POP σ equal but

uko, idep POP σ unequal and

uko, dep POP σ eual ut uko

-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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