1 doing statistics for business doing statistics for business data, inference, and decision making...

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DoingDoing Statistics for BusinessStatistics for Business Data, Inference, and Decision Making

Marilyn K. PelosiTheresa M. Sandifer

Chapter 9Chapter 9Inferences: OneInferences: One

Population 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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Chapter 9 Objectives (con’t)

The Relationship Between Hypothesis Testing and Confidence Intervals

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TRY IT NOW!The Soda MachineTest of Population Mean When

Is UnknownIn 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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TRY IT NOW!The Soda MachineTest of Population Mean When

Is Unknown (con’t)

32.12 32.04 32.04 32.00 32.01 32.1232.13 32.05 32.05 31.72 32.08 32.0332.02 32.22 32.22 32.22 31.89 32.2031.73 31.95 31.95 32.07 32.13 32.1331.98 32.21 32.21 31.97 32.09 31.97

Is there any evidence to indicate that the machine is not filling the bottlesproperly? Use = 0.05.

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Figure 9.1 RejectionRegion for a Lower-TailTest of

Figure 9.2 RejectionRegion 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 (con’t)

Should you accept the shipment? Use = 0.05

0.5053 0.5098 0.4606 0.46060.4711 0.4627 0.4800 0.48000.4672 0.5642 0.5495 0.54950.4672 0.5346 0.5745 0.57450.5340 0.3767 0.3933 0.3933

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Figure 9.3 A Chi-Square Distribution

Figure 9.4Rejection Region for aTwo-Sided Test of theVariance

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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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TRY IT NOW!Poll of Americans

Test of ProportionShe 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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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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TRY IT NOW!The Soft Drink Company

One-Tail Test of ProportionThe 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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Discovery Exercise 9.1Exploring the Connection BetweenConfidence Intervals & Hypothesis Testing

Part IA recent survey is offering the first evidence that PCs are replacing TVsas the primary source of home recreation, information, and entertainment.The survey was conducted among 1200 homes nationwide. The averagecomputer 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 9.1Exploring the Connection BetweenConfidence Intervals & Hypothesis Testing (con’t)Assume that the standard deviation of hours spent in front of a PC is 3hours/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 9.1Exploring the Connection BetweenConfidence 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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Discovery Exercise 9.1Exploring the Connection BetweenConfidence Intervals & Hypothesis Testing (con’t)

Part IIThe Casual Businesswear Employee Survey was conducted to assess theattitudes and behavior of white-collar employees whose companies allowcasual dress on some basis. The study was national in scope and thesample size was 752 people. Of those sampled, 609 agree that allowingcasual dress improves morale.

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(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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Part IIISummarize. Based on these two situations, speculate how you wouldcomplete the following statements:

If the value of the parameter being tested (the one in the nullhypothesis) is not in the confidence interval then I will ______________the null hypothesis.

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If the value of the parameter being tested (the one in the nullhypothesis) 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 Testing>One 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 MeanPopulation VariancePopulation 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 (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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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.

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