MARKETING RESEARCH PART 16 pptx

Sample statistic mean or percentage generated from sample data 2.. Standard error variance divided by sample size; formula for standard error of the mean and another formula for stand

Generalizing a

Sample’s Findings to Its Population and Testing Hypotheses About Percents and

Statistics Versus Parameters

• Statistics: values that are computed

from information provided by a sample

• Parameters: values that are computed from a complete census which are

considered to be precise and valid

measures of the population

to know” about a population Statistics are used to estimate population

The Concepts of Inference and

Statistical Inference

• Inference: drawing a conclusion

based on some evidence

• Statistical inference: a set of

procedures in which the sample size and sample statistics are used to

make estimates of population

parameters

How to Calculate Sample Error

(Accuracy)

n

pq z

error =

sp

Where z = 1.96 (95%)

or 2.58 (99%) Sample Size and Accuracy

Accuracy Levels for Different

population mean or population

percentage is likely to take on

Parameter Estimation

values:

1 Sample statistic (mean or percentage

generated from sample data)

2 Standard error (variance divided by

sample size; formula for standard error

of the mean and another formula for standard error of the percentage)

3 Confidence interval (gives us a range

within which a sample statistic will fall

Parameter Estimation

• Statistics are generated from sample data and are used to estimate population

parameters.

• The sample statistic may be either a

percentage, i.e., 12% of the respondents stated they were “very likely” to patronize a new, upscale restaurant OR

• The sample statistic may be a mean, i.e., the average amount spent per month in

restaurants is $185.00

Parameter Estimation

formulas, one for a percentage and the other for a mean, both formulas have a measure of variability divided

by sample size Given the sample

size, the more variability, the greater the standard error

Parameter Estimation

more precisely our sample statistic

will represent the population

parameter Researchers have an

opportunity for predetermining

standard error when they calculate

the sample size required to

accurately estimate a parameter

Recall Chapter 13 on sample size

Standard Error of the Mean

Standard Error of the

Percentage

Parameter Estimation

• Confidence intervals: the degree of accuracy desired by the researcher and stipulated as a level of

confidence in the form of a

percentage

• Most commonly used level of

confidence: 95%; corresponding to 1.96 standard errors

Parameter Estimation

we can say that if we did our study

over 100 times, we can determine a range within which the sample

statistic will fall 95 times out of 100

(95% level of confidence) This gives

us confidence that the real population value falls within this range

• Theoretical notion

How do I interpret the confidence

interval?

2.5% 2.5%

95%

Parameter Estimation

confidence intervals for a mean or percentage:

sample for that statistic

Parameter Estimation

determine the upper and lower boundaries of the confidence interval range

Parameter Estimation Using SPSS: Estimating a Percentage

RADPROG) and you find that 41.3% listen to “Rock” music

of the population that listens to

“Rock” falls between 36.5% and

How to Compute a Confidence

Interval for a Percent

n

pq z

p −

n

pq z

p +

Estimating a Population Percentage with SPSS

results?

– Our best estimate of the population percentage that prefers “Rock” radio

is 41.3 percent, and we are 95 percent confident that the true population value is between 36.5

Parameter Estimation Using SPSS: Estimating a Mean

interval around a mean sample

statistic

assume

who stated “very likely” to patronize

an upscale restaurant spend in restaurants per month (See p

Parameter Estimation Using SPSS: Estimating a Mean

CASES to select LIKELY=5

MEANS, ONE SAMPLE T-TEST

when you have interval or ratio data

Parameter Estimation Using SPSS: Estimating a Percentage

not calculate for a percentage You must run FREQUENCIES to get your sample statistic and n size Then use

the percentage of the population that listens to “Rock” radio

Estimating a Population Percentage with SPSS

accurately the sample statistic

estimates the percent listening to

“Rock” music

– Our “best estimate” of the population

percentage is 41.3% prefer “Rock”

music stations (n=400) We run FREQUENCIES to learn this.

– But how accurate is this estimate of the

true population percentage preferring

Estimating a Population Mean

with SPSS

– My best estimate is that those “very

likely” to patronize an upscale restaurant in the future, presently spend

$281 dollars per month in a restaurant

In addition, I am 95% confident that the true population value falls between $267 and $297 (95% confidence interval)

Therefore, Jeff Dean can be 95%

confident that the second criterion for

Hypothesis Testing

• Hypothesis: an expectation of what the population parameter value is

• Hypothesis testing: a statistical

procedure used to “accept” or “reject” the hypothesis based on sample

information

• Intuitive hypothesis testing: when

someone uses something he or she has observed to see if it agrees with

or refutes his or her belief about that

Hypothesis Testing

you believe exists in the population

determine the sample statistic

hypothesized parameter

Hypothesis Testing

supports the original hypothesis

hypothesis, revise the hypothesis

to be consistent with the sample’s statistic

What is a Statistical Hypothesis?

expects (or hypothesizes) the

population percent or the average

to be

fall in the confidence interval

fall outside the confidence interval

How a Hypothesis Test Works

Test hypothesis

How to Test Statistical

Testing a Hypothesis of a Mean

hypothesizes that college interns

make $2,800 in commissions A

survey shows $2,750 Does the

survey sample statistic support or fail

to support Rex’s hypothesis? (p 472)

• Since 1.43 z falls between -1.96z and +1.96 z, we ACCEPT the hypothesis.

How to Test Statistical

s

p z

H p H

s

x z

H x H

• The probability that our sample mean

of $2,800 came from a distribution of means around a population parameter

of $2,750 is 95% Therefore, we

accept Rex’s hypothesis

Hypothesis Testing

• Non-Directional hypotheses:

hypotheses that do not indicate the

direction (greater than or less than) of

a hypothesized value

Using SPSS to Test Hypotheses

About a Percentage

percentages; you must use the

formula See p 475

Using SPSS to Test Hypotheses

About a Mean

to test that those stating “very likely” to patronize an upscale restaurant are

willing to pay an average of $18 per

entrée

SAMPLE T TEST

What if We Used a Directional

Hypothesis?

patronize an upscale restaurant are willing to pay more than an average

of $18 per entrée

hypothesized direction? For “more than” hypotheses it should be +; if

not, reject

What if We Used a Directional

Hypothesis?

direction, we are only concerned with one side of the normal distribution Therefore, we need to adjust the

critical values We would accept this

hypothesis if the z value computed is

greater than +1.64 (95%)