Don’t cry because it is all over, smile because it

happened

Potential Problems in Potential Problems in SamplingSampling

Poor Sampling Frame

Cost of Sampling

Built -In Bias

Cost of SamplingCost of Sampling

Money

Time

Wide Geographic Region

Major Errors in Major Errors in SamplingSampling

Bias:

Consistent, repeated divergence in the same direction of a sample statistic from its associated population parameter.

Lack of Precision:

Large theoretical variation in a sample statistic

Sampling ErrorSampling Error

The difference between the sample statistic and its corresponding population

parameter.

Population:

97, 103, 96, 99, 105

(Mean = 100)

Non-Sampling ErrorsNon-Sampling Errors

Survey Timing

Survey Mode

Interviewer – Subject Relationship

Survey Topic

Question Wording

Question Sequence

Statistical SignificanceStatistical Significance

An observed effect so large that it would rarely occur by

chance.

Hypothesis TestingHypothesis Testing

What is a Hypothesis?

A statement about the value of a population parameter developed for the

purpose of testing.

Hypothesis TestingHypothesis TestingWhat is Hypothesis Testing?

A procedure, based on sample evidence and probability theory, used to determine whether the

hypothesis is a reasonable statement and should not be

rejected or is unreasonable and should be rejected.

Hypothesis TestingHypothesis Testing

Examples of hypotheses made about a population parameter are:

• The mean monthly income for systems analysts is $3,625.

• Twenty percent of all juvenile offenders are caught and sentenced to prison.

Hypothesis TestingHypothesis Testing

Null Hypothesis H0:

A statement about the value of a population parameter.

Alternative Hypothesis H1:

A statement that is accepted if the sample data provide evidence that the null hypothesis is false.

Hypothesis TestingHypothesis Testing

Level of Significance:

The probability of rejecting the null hypothesis when it is actually true.

Hypothesis TestingHypothesis Testing

Statistical testing is often done by testing a hypothesis that you expect

to reject.

Null HypothesisNull HypothesisNull Hypothesis H0: A statement about

the value of a population parameter. Stating the current fact(s).

PopulationPopulation

Graphic RepresentationGraphic Representationof the Populationof the Population

Alternative HypothesisAlternative HypothesisAlternative (Research) Hypothesis H1:

A statement that is accepted if the sample data provide evidence that the null hypothesis is false.

SampleSample

Graphic Representation Graphic Representation of a Large Sampleof a Large Sample

Graphic Representation of Graphic Representation of the Population & Samplethe Population & Sample

Sample

ZPopulationZ

Statistics! Statistics! Statistics! Finish the Maze and we get to take a break!

Testing a HypothesisTesting a Hypothesis

Tail Tail

Testing a HypothesisTesting a Hypothesis.05 level of significance.05 level of significance

One tailed test: More than; greater than; larger than; etc…

Critical Z

1.645ZCritical Value

Critical Region.05 Area

Null Hypothesis Area

One Tailed Test, .05Smaller than; less than, etc.

Critical Z

1.645 ZZ value

Critical Region

Null Hypothesis Area

Two Tailed Test, .05Not Equal to; Different Than

Critical Z Critical Z

1.96 ZZ value

1.96 ZZ value

+

Critical RegionCritical Region

Null Hypothesis Area

Graphic RepresentationGraphic Representation of Hypothesis Test Resultsof Hypothesis Test Results

This maze is longer than I thought.

Go Ahead and take a break!

Hypothesis TestingHypothesis TestingState null and alternative hypothesis

Select a level of significance

Formulate a decision rule

Identify the test statistic

Take a sample, arrive at a decision(Reject or fail to reject the null)

Test for Sample Means

X = Sample meanμ = Hypothesized population mean

s = Sample standard deviationN = Sample size

S

One Sample Mean Problem

A recent article in Vitality magazine reported that the mean amount of leisure time per

week for American men is 40.0 hours. You believe this figure is too large and decide to conduct your own test. In a random sample

of 60 men, you find that the mean is 37.8 hours of leisure per week with a standard

deviation of 12.2 hours. Can you conclude that the data in the article is too large? Use

the .05 significance level.

Step 1

State the null and alternative hypothesis.

H0: Mean = 40.0 hours

H1: Mean < 40.0 hours

Step 2

Select a level of significance.

This will be given to you. In this problem, it is .05.

Step 3Establish critical region by converting level of

significance to a Z score..5000 - .0500 = .4500 = 1.64z

If the test statistic falls below -1.64z, the null hypothesis will be rejected.

Step 4Identify the test statistic.

Z = 37.8 – 40.0 12.2 / 7.75

Z = -2.2 / 1.57

Test Statistic: Z = -1.40

Step 5Arrive at a decision.

The test statistic falls in the null hypothesis region. Therefore, we fail to

reject the null.

Test for Two Sample Means

Xi = Mean for group i

Si = Standard deviation for group i

ni = Number in group i

Two Sample Means ProblemThe board of directors at the Anchor Pointe Marina

is studying the usage of boats among its members. A sample of 30 members who have boats 10 to 20 feet in length showed that they

used their boats an average of 11 days last July. The standard deviation of the sample was 3.88

days. For a sample of 40 member with boats 21 to 40 feet in length, the average number of days

they used their boats in July was 7.67 with a standard deviation of 4.42 days. At the .02 significance level, can the board of directors

conclude that those with the smaller boats use their crafts more frequently?

Step 1

State the null and alternative hypothesis.

H0: Large boat usage = small boat usage

H1: Smaller boat usage > large boat usage

Step 2

Select a level of significance.

This will be given to you. In this problem it is .02.

Step 3

Formulate a decision rule.

.5000 - .0200 = .4800 = 2.05z

Step 4Identify the test statistic.

11 – 7.67 = 3.35z

3.882 + 4.422

30 40

Step 5

Arrive at a decision.

The test statistic falls in the critical region, therefore we reject the null.

p-Value in Hypothesis Testing

• p-Value: The probability, assuming that the null hypothesis is true, of getting a value of the test statistic at least as extreme as the computed value for the test.

• If the p-value area is smaller than the significance level, H0 is rejected.

• If the p-value area is larger than the significance level, H0 is not rejected.

Statistical Significance

p-Value: The probability of getting a sample outcome as far from what we would expect to get if the null hypothesis is true.

The stronger that p-value, the stronger the evidence that the null hypothesis is false.

Statistical Significance

P-values can be determined by

- computing the z-score

- using the standard normal table

The null hypothesis can be rejected if the p-value is small enough.

P-Value

1.64 Z 2.05Z