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1 Doing Statistics for Business Doing Statistics for Business Data, Inference, and Decision Making Marilyn K. Pelosi Theresa M. Sandifer Chapter 9 Inferences: One Population

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2 Doing Statistics for Business Chapter 9 Objectives Ü Hypothesis Test of the Population Mean, : Small Sample Ü Hypothesis Test of the Population Variance, 2 Ü Hypothesis Test of the Population Proportion,

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3 Doing Statistics for Business Chapter 9 Objectives (con’t) Ü The Relationship Between Hypothesis Testing and Confidence Intervals

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4 Doing Statistics 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:

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5 Doing Statistics 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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6 Doing Statistics for Business 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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7 Doing Statistics 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

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8 Doing Statistics 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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9 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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10 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 oz 2. A random sample of 20 boxes has a standard deviation of s = 0.25 oz. Use = 0.05.

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11 Doing Statistics 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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12 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.

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13 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 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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14 Doing Statistics 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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15 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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16 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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17 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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18 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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19 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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20 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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21 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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22 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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23 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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24 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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25 Doing Statistics for Business KaddStat Dialog Box

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26 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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27 Doing Statistics for Business Completed KaddStat Dialog Box

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28 Doing Statistics for Business Chapter 9 Summary In this chapter you have learned: 4 How to do a hypothesis test of the: Population Mean Population Variance Population Proportion 4 The differences in the test are in the rejection regions, and the calculations of the test statistic.

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29 Doing Statistics for Business Chapter 9 Summary (con’t) 4 For a test of the Population Mean, use a Z test if the population standard deviation is known; otherwise use a t test. 4 For a test of the Population Variance, use a chi- square test 4 For a test of Proportions use a Z test.

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30 Doing Statistics for Business Chapter 9 Summary (con’t) 4 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 . 4 Use p values to handle potential unethical uses of hypothesis testing and to provide management with more information.

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Fundamentals of Hypothesis Testing: One-Sample Tests

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