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Doing Statistics for Business Data, Inference, and Decision Making Marilyn K. Pelosi Theresa M. Sandifer. Chapter 9 Inferences: One Population . Doing Statistics for Business. Chapter 9 Objectives Hypothesis Test of the Population Mean,  : Small Sample

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DoingStatistics for BusinessData, Inference, and Decision MakingMarilyn K. PelosiTheresa M. Sandifer

Chapter 9

Inferences: One

Population

doing statistics for business
DoingStatistics 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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DoingStatistics for Business

Chapter 9 Objectives (con’t)

  • The Relationship Between Hypothesis Testing and Confidence Intervals
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DoingStatistics for Business

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:

doing statistics for business5
DoingStatistics for Business

TRY IT NOW!

The Soda Machine

Test of Population Mean When 

Is Unknown (con’t)

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 

DoingStatistics for Business
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DoingStatistics for Business

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

doing statistics for business8
DoingStatistics for Business

TRY IT NOW!

Diameter of Washers

Lower-Tail Test of : Small Sample(con’t)

Should you accept the shipment? Use  = 0.05

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Figure 9.3

A Chi-Square

Distribution

Figure 9.4

Rejection Region for a

Two-Sided Test of the

Variance

DoingStatistics for Business
doing statistics for business10
DoingStatistics 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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DoingStatistics for Business

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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Doing Statistics for Business

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.

doing statistics for business13
DoingStatistics 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 you’ve 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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DoingStatistics for Business

TRY IT NOW!

Poll of Americans

Test of Proportion (cont’d)

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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DoingStatistics 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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Doing Statistics for Business

Discovery Exercise 9.1

Exploring the Connection Between

Confidence Intervals & Hypothesis

Testing (con’t)

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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Doing Statistics for Business

Discovery Exercise 9.1

Exploring the Connection Between

Confidence Intervals & Hypothesis

Testing (con’t)

(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 (con’t)

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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Doing Statistics for Business

Discovery Exercise 9.1

Exploring the Connection Between

Confidence Intervals & Hypothesis

Testing (con’t)

(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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Doing Statistics for Business

Discovery Exercise 9.1

Exploring the Connection Between

Confidence Intervals & Hypothesis

Testing (con’t)

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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Doing Statistics for Business

Discovery Exercise 9.1

Exploring the Connection Between

Confidence Intervals & Hypothesis

Testing (con’t)

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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Doing Statistics for Business

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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Doing Statistics for Business

Small Sample Tests for the Population Mean in KaddStat

1. From the Kadd menu choose Hypothesis Testing>One Sample

2. Choose Population Mean using t

3. The dialog box shown on the next slide will open.

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Doing Statistics for Business

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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Doing Statistics for Business

Completed KaddStat Dialog Box

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Doing Statistics for Business

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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Doing Statistics for Business

Chapter 9 Summary (con’t)

  • 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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Doing Statistics for Business

Chapter 9 Summary (con’t)

  • 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.