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

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Doing Statistics for Business Data, Inference,
and Decision MakingMarilyn K. PelosiTheresa M.
Sandifer
Chapter 9 Inferences One Population

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Doing Statistics for Business

• Chapter 9 Objectives
• Hypothesis Test of the Population Mean, ? Small
  Sample
• Hypothesis Test of the Population Variance, ?2
• Hypothesis Test of the Population Proportion, ?

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Doing Statistics for Business

• Chapter 9 Objectives (cont)
• The Relationship Between Hypothesis Testing and
  Confidence Intervals

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• TRY IT NOW!
• The Soda Machine
• Test of Population Mean When ?
• Is Unknown
• In Chapter 8 we looked at the hypothesis test to
  see if a soda machine was
• correctly dispensing 32 oz of soda. The amount
  dispensed is assumed to
• be normally distributed. The machine was not
  working properly if the
• bottles were overfilled or underfilled. You
  observed the machine filling
• 30 bottles and collected the following data

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Doing Statistics for Business

• TRY IT NOW!
• The Soda Machine
• Test of Population Mean When ?
• Is Unknown (cont)

Is there any evidence to indicate that the
machine is not filling the bottles properly? Use
? 0.05.
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• Figure 9.1 Rejection
• Region for a Lower-Tail
• Test of ?

• Figure 9.2 Rejection
• Region for an Upper-
• Tail Test of ?

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• TRY IT NOW!
• Diameter of Washers
• Lower-Tail Test of ? Small Sample
• Your company purchases washers. It is important
  that the diameter
• of the hole not be more than 0.5 inch. If the
  hole in the center of the
• washer is too large then your company will not be
  able to use the washer.
• The diameters are assumed to be normally
  distributed. You have just
• received a shipment of 10,000 of these washers.
  You decide to sample
• 20 to check to be sure that the diameters are not
  more than 0.5 inch, on the
• average. Your measurements (in inches) are

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• TRY IT NOW!
• Diameter of Washers
• Lower-Tail Test of ? Small Sample (cont)
• Should you accept the shipment? Use ? 0.05

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Doing Statistics for Business

• Figure 9.3
• A Chi-Square
• Distribution

• Figure 9.4
• Rejection Region for a
• Two-Sided Test of the
• Variance

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Doing Statistics for Business

• TRY IT NOW!
• The Cereal Company
• Testing the Variance
• A cereal manufacturer wishes to test if the
  population variance of the
• weight of the boxes is equal to 0.0500 oz2. A
  random sample of 20
• boxes has a standard deviation of s 0.25 oz.
  Use ? 0.05.

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Lower-tail test of the variance
Upper-tail test of the variance
Figure 9.5 Rejection Regions for One-sided Tests
of the Variance
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• 5-Step Hypothesis Testing Procedure
• Step 1 Set up the null and alternative
  hypotheses.
• Step 2 Define the test procedure.
• 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

• TRY IT NOW!
• Poll of Americans
• Test of Proportion
• She did it again. For the zillionith time, your
  mother casually asked you when you are going to
  get married and youve been seething ever since.
  How do you get it off your chest? These days, you
  might e-mail her. The Pew Internet and American
  Life Project, based on a telephone survey of
  3,533 randomly selected adults recently (July,
  2000) calculated that 64 million of us e-mail our
  family members.

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Doing Statistics for Business

• TRY IT NOW!
• Poll of Americans
• Test of Proportion (contd)
• Thirty-one percent of those who send family
  e-mail find it an easier way to say frank or
  unpleasant things to their relatives.
• Is there evidence that more than 30 of those
  who send family e-mail use it to communicate
  unpleasant things? Use ? 0.05.

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Doing Statistics for Business

• TRY IT NOW!
• The Soft Drink Company
• One-Tail Test of Proportion
• The Coca-Cola Company is interested in entering
  the fruit drink
• market. Before bringing its new product,
  Fruitopia, to the market the
• company wishes to be sure that it will capture
  more than 20 of the fruit
• drink market. A survey of 1000 people shows that
  230 respondents prefer
• Fruitopia to other fruit drinks. Is there enough
  evidence to allow Coca
• Cola to proceed with the new product? Use ?
  0.05.

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Doing Statistics for Business

• Discovery Exercise 9.1
• Exploring the Connection Between
• Confidence Intervals Hypothesis
• Testing
• Part I
• A recent survey is offering the first evidence
  that PCs are replacing TVs
• as the primary source of home recreation,
  information, and entertainment.
• The survey was conducted among 1200 homes
  nationwide. The average
• computer user spends 9.5 hours per week in front
  of the PC but only 8
• hours per week watching prime-time TV.

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• Discovery Exercise 9.1
• Exploring the Connection Between
• Confidence Intervals Hypothesis
• Testing (cont)
• Assume that the standard deviation of hours spent
  in front of a PC is 3
• hours/week.
• (a) Test the hypothesis that the average number
  of hours per week a computer user spends in
  front of a PC is different from 8 hours.
• Use ? 0.05.

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• Discovery Exercise 9.1
• Exploring the Connection Between
• Confidence Intervals Hypothesis
• Testing (cont)
• (b) Test the hypothesis that the average number
  of hours per week a computer user spends in
  front of a PC is different from 8 hours.
• Use ? 0.05.
• ( c) Is the value of 8 in the confidence
  interval you constructed in part (b)?
• (d) Did you reject the null hypothesis in part
  (a)?

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Doing Statistics for Business

• Discovery Exercise 9.1
• Exploring the Connection Between
• Confidence Intervals Hypothesis
• Testing (cont)
• Part II
• The Casual Businesswear Employee Survey was
  conducted to assess the
• attitudes and behavior of white-collar employees
  whose companies allow
• casual dress on some basis. The study was
  national in scope and the
• sample size was 752 people. Of those sampled,
  609 agree that allowing
• casual dress improves morale.

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• Discovery Exercise 9.1
• Exploring the Connection Between
• Confidence Intervals Hypothesis
• Testing (cont)
• (a) Test the hypothesis that the proportion of
  white-collar employees who agree that allowing
  casual dress improves morale is different from
  80. Use ? 0.05.
• (b) Construct a 95 confidence interval for ?.
• ( c) Is the value of 0.80 in the confidence
  interval?
• (d) Did you fail to reject the null hypothesis?

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• Discovery Exercise 9.1
• Exploring the Connection Between
• Confidence Intervals Hypothesis
• Testing (cont)
• Part III
• Summarize. Based on these two situations,
  speculate how you would
• complete the following statements
• If the value of the parameter being tested (the
  one in the null
• hypothesis) is not in the confidence interval
  then I will ______________
• the null hypothesis.

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• Discovery Exercise 9.1
• Exploring the Connection Between
• Confidence Intervals Hypothesis
• Testing (cont)
• If the value of the parameter being tested (the
  one in the null
• hypothesis) is in the confidence interval then I
  will ______________
• the null hypothesis.

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• Hypothesis Testing in KaddStat
• KaddStat provides statistical functions that
  allow you to perform hypothesis tests for both
  means and proportions.
• The basic steps are the same for each. The only
  differences are the input that the user must
  supply. We will give detailed directions for the
  small sample hypothesis test for the mean. Once
  you understand this procedure, the others are
  very similar.

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• Small Sample Tests for the Population Mean in
  KaddStat
• 1. From the Kadd menu choose Hypothesis
  TestinggtOne Sample
• 2. Choose Population Mean using t
• 3. The dialog box shown on the next slide will
  open.

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KaddStat Dialog Box
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• 1. Null Hypothesis- input the value of the
  hypothesized mean - 5 seconds.
• 2. Alternative Hypthesis -identify the form of
  the alternative hyothesis- click the radio button
  next to Not equal
• 3. Data/user- indicate that you have the raw data
  so click the button labeled Input Range. Click
  on Header Row Included if your data range is
  labeled with a variable name.
• 4. Indicate where you want the results to be
  located.

Three Main Parts of the Dialog Box
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Completed KaddStat Dialog Box
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• Chapter 9 Summary
• In this chapter you have learned
• How to do a hypothesis test of the
• Population Mean
• Population Variance
• Population Proportion
• The differences in the test are in the rejection
  regions, and the calculations of the test
  statistic.

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• Chapter 9 Summary (cont)
• For a test of the Population Mean, use a Z test
  if the population standard deviation is known
  otherwise use a t test.
• For a test of the Population Variance, use a
  chi-square test
• For a test of Proportions use a Z test.

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• Chapter 9 Summary (cont)
• In any hypothesis test the rejection region and
  the final decision depend on the value of ?. You
  can alter the outcome of the test by adjusting
  the value of ?.
• Use p values to handle potential unethical uses
  of hypothesis testing and to provide management
  with more information.