Exploring Marketing Research William G. Zikmund

Exploring Marketing Research William G. Zikmund
Chapter 17: Determining Sample Size

What does Statistics Mean?
Descriptive Statistics Number of People Trends in Employment Data Inferential Statistics Make an inference about a population from a sample Copyright © 2000 by Harcourt, Inc. All rights reserved.

Population Parameter Versus Sample Statistics
Copyright © 2000 by Harcourt, Inc. All rights reserved.

Copyright © 2000 by Harcourt, Inc. All rights reserved.
Population Parameter Variables in a population Measured characteristics of a population Greek lower-case letters as notation Copyright © 2000 by Harcourt, Inc. All rights reserved.

Frequency Distribution of Deposits Frequency (number of people making deposits Amount in each range) less than $3, $3,000 - $4, $5,000 - $9, $10,000 - $14, $15,000 or more 3,120 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Measures of Central Tendency
Mean - Arithmetic Average µ, population; , sample Median - Midpoint of the Distribution Mode - the Value that occurs most often Copyright © 2000 by Harcourt, Inc. All rights reserved.

Measures of Dispersion
The Range Standard Deviation Copyright © 2000 by Harcourt, Inc. All rights reserved.

Measures of Dispersion or Spread
Range Mean absolute deviation Variance Standard deviation Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Range as a Measure of Spread
The range is the distance between the smallest and the largest value in the set. Range = largest value – smallest value Copyright © 2000 by Harcourt, Inc. All rights reserved.

Mean Squared Deviation

Sample Standard Deviation

The Normal Distribution
Normal Curve Bell Shaped Almost all of its values are within plus or minus 3 standard deviations I.Q. is an example Copyright © 2000 by Harcourt, Inc. All rights reserved.

Normal Distribution Conventional Product Adoption Life Cycle: Five types of customers who will end up adopting a product INNOVATORS (2.5%): People who are the first to adopt a product. They are trend-setting, risk-taking, and are not typical consumers. Example: See a movie first weekend it’s out or in a preview. EARLY ADOPTERS (13.5%): People who are among the first but not as risk-taking. They adopt ideas early but with consideration, and they enjoy roles as opinion leaders. They spread the word about the product. Example: See a movie the first week of its release. EARLY MAJORITY (34%): Deliberate customers; adopt earlier than most customers but are not leaders. Example: See a movie after a few weeks, after reading all the reviews and getting recommendations from early adopters. LATE MAJORITY (34%): Skeptical customers, will only adopt an idea if the majority of people have tried it. Example: See a movie after it has been nominated for an Oscar. LAGGARDS (16%): Tradition-bound, suspicious of change; will adopt an idea only after it has been around long enough. Example: See a movie after it has come out on video. MEAN Copyright © 2000 by Harcourt, Inc. All rights reserved.

Normal Distribution 13.59% 13.59% 34.13% 34.13% Conventional Product Adoption Life Cycle: Five types of customers who will end up adopting a product INNOVATORS (2.5%): People who are the first to adopt a product. They are trend-setting, risk-taking, and are not typical consumers. Example: See a movie first weekend it’s out or in a preview. EARLY ADOPTERS (13.5%): People who are among the first but not as risk-taking. They adopt ideas early but with consideration, and they enjoy roles as opinion leaders. They spread the word about the product. Example: See a movie the first week of its release. EARLY MAJORITY (34%): Deliberate customers; adopt earlier than most customers but are not leaders. Example: See a movie after a few weeks, after reading all the reviews and getting recommendations from early adopters. LATE MAJORITY (34%): Skeptical customers, will only adopt an idea if the majority of people have tried it. Example: See a movie after it has been nominated for an Oscar. LAGGARDS (16%): Tradition-bound, suspicious of change; will adopt an idea only after it has been around long enough. Example: See a movie after it has come out on video. 2.14% 2.14% Copyright © 2000 by Harcourt, Inc. All rights reserved.

Normal Curve: IQ Example
70 85 100 115 145 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Standardized Normal Distribution
Symetrical about its mean Mean identifies highest point Infinite number of cases - a continuous distribution Area under curve has a probability density = 1.0 Mean of zero, standard deviation of 1 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Standard Normal Curve The curve is bell-shaped or symmetrical About 68% of the observations will fall within 1 standard deviation of the mean About 95% of the observations will fall within approximately 2 (1.96) standard deviations of the mean Almost all of the observations will fall within 3 standard deviations of the mean Copyright © 2000 by Harcourt, Inc. All rights reserved.

A Standardized Normal Curve Conventional Product Adoption Life Cycle: Five types of customers who will end up adopting a product INNOVATORS (2.5%): People who are the first to adopt a product. They are trend-setting, risk-taking, and are not typical consumers. Example: See a movie first weekend it’s out or in a preview. EARLY ADOPTERS (13.5%): People who are among the first but not as risk-taking. They adopt ideas early but with consideration, and they enjoy roles as opinion leaders. They spread the word about the product. Example: See a movie the first week of its release. EARLY MAJORITY (34%): Deliberate customers; adopt earlier than most customers but are not leaders. Example: See a movie after a few weeks, after reading all the reviews and getting recommendations from early adopters. LATE MAJORITY (34%): Skeptical customers, will only adopt an idea if the majority of people have tried it. Example: See a movie after it has been nominated for an Oscar. LAGGARDS (16%): Tradition-bound, suspicious of change; will adopt an idea only after it has been around long enough. Example: See a movie after it has come out on video. z 1 2 -2 -1 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Standardized Normal is the Distribution of Z

Linear Transformation of Any Normal Variable into a Standardized Normal Variable s s m X m Sometimes the scale is stretched Sometimes the scale is shrunk Copyright © 2000 by Harcourt, Inc. All rights reserved.

Population Distribution Conventional Product Adoption Life Cycle: Five types of customers who will end up adopting a product INNOVATORS (2.5%): People who are the first to adopt a product. They are trend-setting, risk-taking, and are not typical consumers. Example: See a movie first weekend it’s out or in a preview. EARLY ADOPTERS (13.5%): People who are among the first but not as risk-taking. They adopt ideas early but with consideration, and they enjoy roles as opinion leaders. They spread the word about the product. Example: See a movie the first week of its release. EARLY MAJORITY (34%): Deliberate customers; adopt earlier than most customers but are not leaders. Example: See a movie after a few weeks, after reading all the reviews and getting recommendations from early adopters. LATE MAJORITY (34%): Skeptical customers, will only adopt an idea if the majority of people have tried it. Example: See a movie after it has been nominated for an Oscar. LAGGARDS (16%): Tradition-bound, suspicious of change; will adopt an idea only after it has been around long enough. Example: See a movie after it has come out on video. -s m s x Copyright © 2000 by Harcourt, Inc. All rights reserved.

Sample Distribution Conventional Product Adoption Life Cycle: Five types of customers who will end up adopting a product INNOVATORS (2.5%): People who are the first to adopt a product. They are trend-setting, risk-taking, and are not typical consumers. Example: See a movie first weekend it’s out or in a preview. EARLY ADOPTERS (13.5%): People who are among the first but not as risk-taking. They adopt ideas early but with consideration, and they enjoy roles as opinion leaders. They spread the word about the product. Example: See a movie the first week of its release. EARLY MAJORITY (34%): Deliberate customers; adopt earlier than most customers but are not leaders. Example: See a movie after a few weeks, after reading all the reviews and getting recommendations from early adopters. LATE MAJORITY (34%): Skeptical customers, will only adopt an idea if the majority of people have tried it. Example: See a movie after it has been nominated for an Oscar. LAGGARDS (16%): Tradition-bound, suspicious of change; will adopt an idea only after it has been around long enough. Example: See a movie after it has come out on video. _ C X S Copyright © 2000 by Harcourt, Inc. All rights reserved.

Sampling Distribution Conventional Product Adoption Life Cycle: Five types of customers who will end up adopting a product INNOVATORS (2.5%): People who are the first to adopt a product. They are trend-setting, risk-taking, and are not typical consumers. Example: See a movie first weekend it’s out or in a preview. EARLY ADOPTERS (13.5%): People who are among the first but not as risk-taking. They adopt ideas early but with consideration, and they enjoy roles as opinion leaders. They spread the word about the product. Example: See a movie the first week of its release. EARLY MAJORITY (34%): Deliberate customers; adopt earlier than most customers but are not leaders. Example: See a movie after a few weeks, after reading all the reviews and getting recommendations from early adopters. LATE MAJORITY (34%): Skeptical customers, will only adopt an idea if the majority of people have tried it. Example: See a movie after it has been nominated for an Oscar. LAGGARDS (16%): Tradition-bound, suspicious of change; will adopt an idea only after it has been around long enough. Example: See a movie after it has come out on video. Copyright © 2000 by Harcourt, Inc. All rights reserved.

Standard Error of the Mean

Estimating the Standard Error of the Mean

Random Sampling Error and Sample Size are Related

Sample Size Formula - example
Suppose a survey researcher, studying expenditures on lipstick, wishes to have a 95 percent confident level (Z) and a range of error (E) of less than $2.00. The estimate of the standard deviation is $29.00. Copyright © 2000 by Harcourt, Inc. All rights reserved.

Standard Error of the Proportion

Confidence Interval for a Proportion

Sample Size for a Proportion

Exploring Marketing Research William G. Zikmund

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