# QMS 102 Study Guide - Final Guide: Central Limit Theorem, Sampling Distribution, Standard Deviation

by OC63619

School

Ryerson UniversityDepartment

Quantitative MethodsCourse Code

QMS 102Professor

Jason Chin- Tiong ChanStudy Guide

FinalThis

**preview**shows pages 1-2. to view the full**8 pages of the document.**Business Statistics I –QMS102 Chapter8

Chapter8 Sampling distributions

Outcomes

1. Discuss the importance of sampling and the main reasons for sampling

2. Explain the definition of sampling distributions

3. Explain the central limit theorem

4. Calculate the standard error of the mean

5. Use the central limit theorem to determine probability of selecting possible

sample means from a specified population

Sampling

1. Select a portion of the population that is most representative of the population

2. Provide sufficient information so that conclusions (inferences) can be drawn

about the characteristics of the population

Reasons for Sampling

1. To contact the whole population would often be time consuming

2. The cost of studying all the items in a population may be prohibitive

3. Some tests could be destructive in nature

If the wine tasters in Niagara-on-the –Lake drank all the wine to evaluate

the vintage, they would consume the entire crop, and none would be

available for sale

4. The sample results are adequate

Example: The Federal Government uses a sample of grocery stores

scattered throughout Canada to determine the monthly index of food

prices. The prices of bread, milk and other major food items are included

in the index. It is unlikely that the inclusion of all grocery stores in Canada

would significantly affect the index, since the prices of milk, bread, and

other major food usually do not vary by more than a few cents from one

chain store to another.

Sampling distributions

1. For any population data set, there is only one value of the population

mean and population standard deviation.

2. Different samples drawn from the same population may result in different

sample mean and sample standard deviation.

3. Sampling distribution is the distribution of all sample statistics.

Fall2012 Page#1

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

Business Statistics I –QMS102 Chapter8

Sampling Distribution of the Mean

1. The distribution of all possible sample means.

Population mean

N

X

N

i

i

∑

=

=1

µ

The average of all sample means,

X

µ

Standard Error of the Mean

The value of the standard deviation of all possible sample means

n

X

σ

σ

=

The Central Limit Theorem

For a large sample size, the sampling distribution of

x

is approximately normal,

irrespective of the shape of the population distribution. The mean and standard

deviation of the sampling distribution of

x

are

µµ

=

X

and

n

X

σ

σ

=

The sample size is usually considered to be large if

30≥n

Finding the Z for the Sampling Distribution of the Mean

n

X

X

Z

X

X

σ

µ

σ

µ

−

=

−

=

Note:

The sampling distribution of the sample mean will follow a normal probability

distribution under two conditions:

1. When the samples are taken from population known to follow a normal

distribution. In this case, the size of the sample is not a factor.

2. When the shape of the population distribution is not known or the shape is

known to be non-normal but the sample contains at least 30 observations.

Fall2012 Page#2

###### You're Reading a Preview

Unlock to view full version

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

Business Statistics I –QMS102 Chapter8

Example1

The mean rent for a one-bedroom apartment in downtown Toronto is $1200 per

month, with a standard deviation of $250. The distribution of the monthly costs

does not follow the normal distribution. In fact, it is positively skewed. What is the

probability of selecting a sample of 50 one-bedroom apartments and finding the

mean to be at least $950 per month?

Fall2012 Page#3

###### You're Reading a Preview

Unlock to view full version