Doing Statistics for Business Data, Inference, and Decision Making Marilyn K. Pelosi Theresa M. Sand

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Doing Statistics for Business Data, Inference,
and Decision MakingMarilyn K. PelosiTheresa M.
Sandifer
Chapter 8 Hypothesis Testing An Introduction

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Doing Statistics for Business

• Chapter 8 Objectives
• What Is a Hypothesis Test?
• Overview of Hypotheses to be Tested
• The Pieces of a Hypothesis Test
• Two-Tail Tests of the Mean Large Sample
• Which Theory Should Go into the Null Hypothesis?

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Doing Statistics for Business

• Chapter 8 Objectives (cont)
• One-Tail Tests of the Mean Large Sample
• What Error Could You be Making?

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Doing Statistics for Business

• What is an Hypothesis Test?
• The word hypothesis has the same meaning in
• statistics as it does in everyday use. What does
  this
• word mean to you? Some possibilities are
• an idea
• an assumption
• a guess
• a theory

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Doing Statistics for Business

• In statistics, a Hypothesis is an idea, an
• assumption, or a theory about
• the characteristics of one or more populations.

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Doing Statistics for Business

• A Hypothesis Test is a statistical procedure
• that involves formulating a hypothesis and
• using sample data to decide on the validity of
• the hypothesis.

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Doing Statistics for Business

• TRY IT NOW!
• 7-11 Stores Possible Hypotheses
• 7-11 stores are located all over the Northeast.
  Management is
• studying sales data. Develop a specific
  hypothesis for each of the
• different types of hypotheses that we have
  discussed. Heres one
• hypothesis to get you started
• Type of Hypothesis Specific Hypothesis
• The shape of the distribution of the
  variable Daily sales at Store 23 are
• in one population normally distributed

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Doing Statistics for Business

• TRY IT NOW!
• The Sports Complex
• Possible Hypotheses
• A particular university is considering building a
  new sports
• complex. It wishes to know if the sports complex
  would be widely used
• by students. Develop a specific hypothesis for
  each of the different types
• of hypotheses that we have discussed.

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Doing Statistics for Business

• The Null Hypothesis is a statement about
• a parameter of the population(s).
• It is referred to as H0.
• The Alternative Hypothesis is a statement
• about a parameter of the population(s) that
• is opposite to the null hypothesis.
• It is referred to as HA.

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Doing Statistics for Business

• TRY IT NOW!
• The Potato Chip Manufacturer
• Setting Up the Null and Alternative
• Hypotheses
• Many people eat chips with their soda. Suppose a
  potato chip
• manufacturer is concerned that the bagging
  equipment may not be
• functioning properly when filling 10-oz bags.
  You have been asked to
• set up a hypothesis test that will help determine
  if there is a problem with
• the bagging equipment. What null and alternative
  hypothesis would you
• use?

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Doing Statistics for Business

• Discovery Exercise 8.1
• Formulating Hypotheses
• Consider the population of all M M packages
  like the
• one you have in your hand.
• Step 1 Identify as many different variables as
  you can. Be sure you have
• some quantitative and some qualitative variables.
  Record the values of
• these variables for your package. (Hint You
  should carefully examine the
• package before you rip it open.)
• Step2 Select one of the quantitative variables
  and set up a null and
• alternative hypothesis for a parameter of this
  variable.

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Doing Statistics for Business

• Discovery Exercise 8.1
• Formulating Hypotheses (cont)
• Step 3 Select one of the qualitative variables
  and set up
• a null and alternative hypothesis for a parameter
  of this variable.
• Step 4 As a class agree on several quantitative
  and qualitative variables
• that you feel are important. Record the data for
  all of the teams on each
• of these variables.
• Step 5 Use the tools of descriptive statistics
  to display these data.
• Step 6 Enjoy the MMs!

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Doing Statistics for Business

• A Test Statistic is calculated from
• the sample data and is used to
• decide between the null and
• alternative hypothesis.

The rejection region is the range of values of
the test statistic that will lead you to reject
the null hypothesis. Alpha, ? , is the area of
the rejection region.
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Doing Statistics for Business

• 5-Step Hypothesis Testing Procedure
• Step 1 Set up the null and alternative
  hypotheses.
• Step 2 Define the test procedure. This includes
  selecting the right test, picking the value of ?,
  and finding the rejection region.
• Step 3 Collect the data and calculate the test
  statistic.
• Step 4 Decide whether or not to reject the null
  hypothesis.
• Step 5 Interpret the statistical decision in
  terms of the stated problem.

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Doing Statistics for Business
Figure 8.1 Possible Rejection Region
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Doing Statistics for Business
Figure 8.2 Rejection Region for a two-tail test
of m
-z a/2
z a/2
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Doing Statistics for Business

• TRY IT NOW!
• The Tissue Company
• Finding the Rejection Region
• Suppose the tissue company decided to set ? at
  0.10.
• Find the rejection region.

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Doing Statistics for Business

• Discovery Exercise 8.2
• Exploring the Impact of Varying
• the Value of ?
• You may remember that in Chapter 4 we examined
  the data collected by a
• company that was concerned about the length of
  time its customers were
• on hold. The data shown below were first
  presented to you in Example
• 4.15 in your textbook. There are 50 observations
  on customer hold times

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Doing Statistics for Business

• Discovery Exercise 8.2
• Exploring the Impact of Varying
• the Value of ? (cont)
• The company wishes to test the hypothesis that
  the true mean hold time is
• 7 minutes. The standard deviation of hold times
  is known to be 2 minutes.
• (a) Test this hypothesis using a value of ?
  0.10.
• (b) Now vary the value of ? and complete the
  following table.
• ? Rejection Region Decision
• 0.10 (from part a above)
• 0.05
• 0.02
• 0.01

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Doing Statistics for Business

• Discovery Exercise 8.2
• Exploring the Impact of Varying
• the Value of ? (cont)
• ( c) What happened to your decision as the value
  of ? changed?

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Doing Statistics for Business

• The p value is defined to be the smallest
• value of ? for which you can reject H0.

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Doing Statistics for Business

• TRY IT NOW!
• The Tissue Company
• Finding the p Value
• Find the p value for the tissue companys
  two-tail test of ?.
• Recall that the average MDStrength was found to
  be 980 lb/ream
• and the Z statistic was calculated to be -2.40.

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Doing Statistics for Business

• A Type I Error is made when you reject the
• null hypothesis and the null hypothesis is
• actually true. In other words, you incorrectly
• reject a true null hypothesis.
• A Type II Error is made when you fail to reject
• the null hypothesis and the null hypothesis is
• false. In other words, you continue to believe a
• false null hypothesis.

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Doing Statistics for Business

• TRY IT NOW!
• The Potato Chip Manufacturer
• Examining the Type I and Type II Errors
• Find the Type I and Type II errors for the
  hypothesis test that you set up
• for the potato chip manufacturer of this chapter.

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Doing Statistics for Business

• The probability of making a Type I Error is
• called ? (alpha).
• The probability of making a Type II Error is
• called ? (beta).

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Doing Statistics for Business

• TRY IT NOW!
• New Package Design
• Setting the Value of ?
• We have seen that a one-sided test is often used
  to investigate
• whether a new method of advertising or producing
  something is better
• than the existing method. Consider a company
  that is trying a new
• package design for its product. The average
  sales for this product are
• currently 1500/month. The null and alternative
  hypotheses would be
• H0. ? ? 1500
• HA. ? gt 1500

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Doing Statistics for Business

• TRY IT NOW!
• New Package Design
• Setting the Value of ? (cont)
• In terms of the companys decision to adopt or
  not adopt this new
• design, what are the Type I and Type II errors?

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Doing Statistics for Business

• A Two-Tail Test of the population mean has
• the following null and alternative hypotheses
• H0 ? a specific number
• HA ? ? a specific number

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Doing Statistics for Business

• TRY IT NOW!
• The Chapperel Steel Company
• Setting Up the Null and Alternative
• Hypotheses for a Two-Tail Test of the Mean
• Another recent management approach is to have
  employees become actual
• partners of the business. Chapperel Steel
  Company has done exactly this
• and the company feels that one of the benefits of
  this concept is that the
• average number of sick days will decrease. Prior
  to implementing this
• program, Chapperel had an average of 7.2 sick
  days per employee. Set up
• the null and alternative hypothesis to test if
  the average number of sick
• days per employee is different from 7.2.

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Doing Statistics for Business

• A Lower-Tail Test of the population mean has
• the following null and alternative hypotheses
• H0 ? ? a specific number
• HA ? lt a specific number

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Doing Statistics for Business

• TRY IT NOW!
• The Bank Example
• Lower-Tail Test
• Suppose a bank knows that their customers are
  waiting in line an average
• of 10.2 minutes during the lunch hour. The
  branch manager has decided
• to add an additional teller during the 12-2 p.m.
  period and wishes to test
• the hypothesis that the average wait has
  decreased due to the additional
• teller. Set up the null and alternative
  hypothesis for the bank manager.

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Doing Statistics for Business

• An Upper-Tail Test of the population mean
• has the following null and alternative
  hypotheses
• H0 ? ? a specific number
• HA ? gt a specific number

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Doing Statistics for Business

• TRY IT NOW!
• New Advertising Program
• Setting Up an Upper-Tail Test
• Suppose a company has implemented a new
  advertising program
• in the hope of increasing sales from last years
  annual average of 4.3
• million. Set up the null and alternative
  hypotheses to test the theory that
• sales have increased.

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Doing Statistics for Business

• Summary A Two-Tail Test
• Is used to test if the parameter has shifted away
  from a certain number in either direction,
  increased or decreased.
• Must always be set up so the theory is the
  null hypothesis.
• Is used when the problem statement has the key
  words changed or different in the problem
  statement.

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Doing Statistics for Business

• Summary A Lower-Tail Test
• Is used to test if the parameter has shifted to
  a number less than a certain number.
• Must always be set up so the as part of the
  null hypothesis.
• Is used when the problem statement has the key
  words decreased, reduced, less than.
• The theory that you wish to prove is placed
  into the alternative hypothesis.

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Doing Statistics for Business

• Summary An Upper-Tail Test
• Is used to test if the parameter has shifted to
  a number more than a certain number.
• Must always be set up so the as part of the
  null hypothesis.
• Is used when the problem statement has the key
  words increased, greater than.
• The theory that you wish to prove is placed
  into the alternative hypothesis.

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Doing Statistics for Business

• TRY IT NOW!
• Judicial System
• Setting Up the Null and Alternative
• Hypothesis
• If you think about the judicial system in terms
  of a hypothesis test, how
• would you set up the null and the alternative
  hypotheses?

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Doing Statistics for Business

• TRY IT NOW!
• VCR Manufacturer
• Setting Up the Hypotheses So the Status
• Quo Is in the Null Hypothesis
• Suppose a manufacturer of VCRs claims that the
  average life of his VCRs
• is at least three years. You have a VCR made by
  this company and have
• had problems with it, and so you question this
  claim. Set up the
• hypothesis test to investigate the manufacturers
  claims.

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Doing Statistics for Business

• TRY IT NOW!
• Finding the Rejection Region
• Try to predict what will happen to the -Z a value
  for the one-tail
• test if ? 0.025. Now find it to confirm your
  guess.

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Doing Statistics for Business

• TRY IT NOW!
• Frozen Foods
• Lower-Tail Test of the Mean
• Jake Bramhall can identify the make, model, and
  number of
• cylinders of any passing car but he cant tell
  the difference between
• stewed tomatoes and tomato paste. While more men
  are pushing shopping
• carts these days, many like Mr.. Bramhall show
  little aptitude in the
• supermarket and display markedly different
  purchasing behavior than
• women.

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Doing Statistics for Business

• TRY IT NOW!
• Frozen Foods
• Lower-Tail Test of the Mean (cont)
• A study done by Consumer Network Inc. shows that
  the average
• amount of money spent by 100 single men on facial
  tissues was 7.38.
• On the basis of these data can you conclude that
  men spend less money on
• facial tissues than the average 8.19 spent by
  women on facial tissues?
• Use a population standard deviation of 3.50 and
  ? value of 0.05. Are the
• results different if you use ? 0.01?

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Doing Statistics for Business

• TRY IT NOW!
• Supermarket Survey
• Upper-Tail Test of the Mean
• From the same supermarket survey it is found that
  the 100 men
• spent, on on the average, 19.98 on low-calorie
  soft drinks. Is there
• enough evidence to conclude that men spend more
  than women, who, on
• the average, spent 18.86? Assume that the
  population standard deviation
• is 10 and use ? 0.05.

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Doing Statistics for Business
Figure 8.3 Rejection Region for a two-tail test
of m with ? 0.05
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Doing Statistics for Business

• Chapter 8 Summary
• In this chapter you have learned
• The key steps in doing any Hypothesis Test begins
  with formulating two opposing viewpoints called
  the Null and Alternative Hypotheses.
• These hypotheses are theories or ideas about the
  value of one or more population parameters.

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Doing Statistics for Business

• Chapter 8 Summary (cont)
• The technique of Hypothesis Testing helps you
  decide between these opposing hypotheses using
  the sample data as the evidence upon which to
  base your decision.
• In doing any hypothesis test there are two
  possible errors you can make
• Type I and
• Type II

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Doing Statistics for Business

• Chapter 8 Summary (cont)
• The probability of making these errors are
  labeled ? and ?, respectively.
• Large Sample Tests are applied whenever you know
  the population standard deviation or if you have
  a sufficiently large sample size, n gt 30.