Population: The entire set of elements of interest (i.e. all humans, all working-age people in Canada, all IT companies). A population parameter is a characteristic used to describe a population. For example, Population mean ( Population standard deviation ( Population median ( The values of the population parameters would be preferable for use in decision-making but seldom will these values be known since collecting all the population elements (a census) is usually too expensive and/or
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Miles/Gallon 21 Miles/Gallon | Price Distribution(Mean, Variance (Sigma)^2) | Normal Distribution(43,215, (2,981) ^2) | Normal Distribution(34,990, (2,367) ^2) | Gas Distribution(A,B) | Uniform Distribution(24,34) Miles/Gallon | Uniform Distribution (25,35) Miles/Gallon | 1- Percentage of Mercedes CLK 320 dealers selling with 42,000 or more: Z-Score = (X-Mean)/Standard Deviation = (42000-43215)/2981= -0.407 = -0.41 By going to the normal distribution table we find that the probability of
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Enrollment | | | | Mean | 165.16 | Standard Error | 28.1682256 | Median | 126 | Mode | 30 | Standard Deviation | 140.841128 | Sample Variance | 19836.22333 | Kurtosis | -0.751273971 | Skewness | 0.756612995 | Range | 451 | Minimum | 12 | Maximum | 463 | Sum | 4129 | Count | 25 | Insights: 1. Average full time enrollment is 165 students and median enrollment is 126 students. 2. It appears that the distribution of full-time enrollments is positively skewed
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The probability distribution of the population data is called the population distribution. Tables 7.1 and 7.2 on page 309 of the text provide an example of such a distribution. The probability distribution of a sample statistic is called its sampling distribution. Tables 7.3 to 7.5 on page 311 of the text provide an example of the sampling distribution of the sample mean. 1. Sampling error is the difference between the value of the sample statistic and the value of the corresponding population
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SAMPLING DISTRIBUTIONS Simple Random Sample A simple random sample X 1 , , X n , taken from a population represented by a random variable X with mean and standard deviation , has the following characteristics. Each X i , i 1,, n , is a random variable that has the same distribution as X, and thus the same mean and standard deviation . The X i ’s are independent random variables implying the following identity: V X 1 X n V X 1 V X n 2 2
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(1.6) Expected value of X, E(X) = PiXi = (1.7) Variance of X, var(X) = Pi(Xi − )2 (1.8) Standard deviation of X, σ(X) = (1.9) Covariance between X and Y, cov(X,Y) = Pi(Xi − )(Yi −) (1.10) Correlation coefficient between X and Y, r(X,Y) =
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The population variance is σ2=600. 9.13. A pharmaceutical manufacturer is concerned that the impurity concentration in pills should not exceed 3%. It is known that from a particular production run impurity concentrations follow a normal distribution with a standard deviation of 0.4%. A random sample of 64 pills from a production run was checked, and the sample mean impurity concentration was found to be 3.07%. a. Test at the 5% level the null hypothesis that the population mean impurity concentration
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1.1) Definition of 'Mode' A statistical term that refers to the most frequently occurring number found in a set of numbers. The mode is found by collecting and organizing the data in order to count the frequency of each result. The result with the highest occurrences is the mode of the set. Other related terms include the mean, or the average of a set; and the median, or the middle value in a set. Investopedia Says Investopedia explains 'Mode' For example, in the following list of numbers, 16 is
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following statements are correct? 1. A normal distribution is any distribution that is not unusual. False 2. The graph of a normal distribution is bell-shaped. True 3. If a population has a normal distribution, the mean and the median are not equal. False 4. The graph of a normal distribution is symmetric. True Using the 68-95-99.7 rule: 34-47.5-49.58 Assume that a set of test scores is normally distributed with a mean of 100 and a standard deviation of 20. Use the 68-95-99.7 rule
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1. Normal Probability Distribution sketch used to approximate the demand distribution with the its mean and Standard Deviation 0.4750 0.4750 0.95 10,000 20,000 30,000 10,000 20,000 30,000 Figure 1: Normal Probability Distribution Curve for Expected demand Expected Demand = 20,000 Hence, Mean () = 20,000 The probability of demand units to be in between 10,000 and 20,000 is 0.95 as also given in the Figure 1. In order to compute Standard Deviation
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