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9/9/11 Statistical Methods for Business  Decision-Making  Statistical Tools See notes page

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9/9/11
9/9/11 Statistical Tools I. Introduction 9 Managers need data to understand their organization and its environment. 9 Describing data can help you gain some of that understanding. 9 However, gaining a fuller understanding of most problems and insight into their solutions usually requires analyzing that data .

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9/9/11 I. Introduction (cont.) Four useful tools for such analysis are covered in this section. 9 The first, the normal distribution , can help answer a broad range of questions. 9 This is true, in part, because many business variables have a bell- shaped distribution of values. 9 The proper name = .
9/9/11 I. Introduction (cont.) The remaining three tools 9 (1) confidence interval & (2) t-test 9 comparing two variables 9 answer questions about differences between the means of two variables. 9 correlation coefficient (r) 9 strength and 9 direction (positive or negative) 9 of the relationship between two variables .

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9/9/11 II. The Normal Distribution Many business variables have a bell- shaped distribution - normal distribution -of values. 9 See Figure 1.
9/9/11 II. The Normal Distribution (c f(x) = height of curve = % of numbers in specific interval x = variable mean of x = µ 1 2 1 6 Normal Curve

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9/9/11 II. The Normal Distribution (con The normal distribution can be fully described by two values: 9 its mean µ (mu) and 9 its standard deviation & (sigma) or, equivalently, its variance ± 2 . 9 Each and every variable with a normal distribution has certain characteristics . 9 These characteristics are worth covering since they are the basis for answering
9/9/11 II. The Normal Distribution (con A. Characteristics 9 symmetric around vertical line at x = µ 9 area to right of mean is ½ of total area under curve; area to left of mean is ½ of total area under curve (see next slide) 9 different values for µ (mean) & q 2 (variance) determine different curves 9 µ determines where curve centered & 9 92 determines how spread out curve is

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9/9/11 II. The Normal Distribution (con f(x ) x symmetric around vertical line at x = µ µ
9/9/11 II. The Normal Distribution (cont.) f(x ) x area to left of mean is 1/2 of total area; area to right of mean is 1/2 of total area 1/2 of total area µ 1/2 of total area

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9/9/11 The Normal Distribution (cont.) The probability of the random variable being a value within some given interval from x 1 to x 2 is 9 area under the graph between x 1 and x2. 0 .83 Area = .2967 x P(0 <   x  <  0.83) = 29.67%
9/9/11 II. The Normal Distribution (con (covered in Section 4. “Describing Data ”) 9 4. approximately 68% of area under normal curve is within one standard deviation of mean 9 5. approximately 95% of area under normal curve is within two standard deviations of mean 9 6. approximately 99.7% of area under normal curve is within three standard deviations of mean

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9/9/11 68% of the distribution’s values, within one standard deviation  68% µ µ - s µ + s f(x) x Areas Under Normal Curve
9/9/11 95% of the values, within 2 standard deviations of the mean 68% 95% µ µ - s µ + s µ - 2s µ + 2s f(x) x Areas Under Normal Curve

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7tools - DecisionMaking Statistical Tools See notes page...

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