# QMS 202 Study Guide - Final Guide: Confidence Interval, Standard Deviation, Test Statistic

by OC218876

School

Ryerson UniversityDepartment

Quantitative MethodsCourse Code

QMS 202Professor

Gunawardena EgodawatteStudy Guide

FinalThis

**preview**shows pages 1-3. to view the full**12 pages of the document.**QMS 202 Final Exam Notes

No Sampling or Normal Distribution

Confidence Intervals

•95% confidence interval: There is 95% confidence that the mean salary of an accountant

falls within the range of the confidence interval constructed for the sample mean salary

•There is 5% chance that the population mean salary will fall outside the confidence limit

•Since we know the population standard deviation, we can use the formula

2

X Z n

α

σ

±

to construct a

(1 ) 100%

α

− ×

confidence interval for the population mean (

µ

) using the

sample mean (

X

).

•Here

2

Z

α

is called the critical value.

•For a 95% confidence interval,

0.05

α

=

and

.025

2

1.96Z Z

α

= =

.

•For a 99% confidence interval

0.01

α

=

and

.005

2

2.58Z Z

α

= =

.

•To find crit value, DIST > NORM > InvN

oTail (doesn’t matter which because it is symmetrical)

oArea: 0.025

oWhen normal distribution is assumed, s.dev is 1, mean is 0

•UNKNOWN population standard deviation

o

σ

is unknown (s.dev of the total) , it is estimated by

s

(s.dev of sample)

o

2

s

X t n

α

±

, df= n-1

•PROPORTION

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

•

2

(1 )p p

p Z n

α

−

±

where p = sample proportion =

X

n

•CALCULATOR METHOD:

oINTR > Z >1-S (s.dev known)

oINTR > t > 1-S (s.dev unknown)

oINTR > Z > 1-P

•*sometimes the sample mean doesn’t fall inside the limit

•Determining sample size

2 2

2

2

Z

ne

α

σ

=

•

2

2

2

(1 )Z

ne

απ π

−

=

•If sample size is a decimal, always round up

Hypothesis Testing – One Sample

•Ho, Null hypothesis ( equals, greater or equal, lesser or equal)

•H1 or Ha, Alternative hypothesis ( not equal, greater, lesser)

oAlways population parameters!

•If the test statistic falls in the critical/rejection region, then we reject the null hypothesis

•If it falls outside the rejection region, there is insufficient evidence to reject Ho

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

o

oRejection region is alpha/2

•Two tail test:

o

0 0

0

:

:

a

H

H

µ µ

µ µ

=

≠

o

STAT

X

Z

n

µ

σ

−

=

oWe reject

0

H

, when

2

STAT

Z Z

α

>

or

2

STAT

Z Z

α

< −

.

•Right tail test

o

0 0

0

:

:

a

H

H

µ µ

µ µ

≤

>

•Left tail test

o

0 0

0

:

:

a

H

H

µ µ

µ µ

≥

<

•Type 1 error

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