excess kurtosis is 0.208336. For the normal distribution‚ skewness is zero. Since the skewness for SCORE variable is negative‚ this indicates that the distribution is skewed to the left (the long tail will be in the negative direction). For the normal distribution‚ kurtosis is three. So K-3 measures excess kurtosis. Since the excess kurtosis for SCORE variable is positive‚ the distribution is leptokurtic (it has thick tails as compared to the normal distribution. Summary Statistics‚ using the observations
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MDM4U – Grade 12 Data Management – Exam Unit 1: One Variable Analysis Types of Data Numerical Data Discrete: consists of whole numbers Ie. Number of trucks. Continuous: measured using real numbers Ie‚ Measuring temperature. Categorical Data: cannot be qualitatively measured Nominal: Data which any order presented makes sense Ie‚ Eye Colour‚ Hair Colour. Ordinal Data: better if sorted or ordered Ie‚ Date and Time‚ scalar options Collecting Data Primary: collected by yourself Secondary:
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Chapter 2—Introduction to Probability PROBLEM 1. A market study taken at a local sporting goods store showed that of 20 people questioned‚ 6 owned tents‚ 10 owned sleeping bags‚ 8 owned camping stoves‚ 4 owned both tents and camping stoves‚ and 4 owned both sleeping bags and camping stoves. Let: Event A = owns a tent Event B = owns a sleeping bag Event C = owns a camping stove and let the sample space be the 20 people questioned. a. Find P(A)‚ P(B)‚ P(C)‚ P(A C)‚ P(B C). b
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get a good idea of the price of rice in the whole nation. Exercise 34 Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110‚000. This distribution follows the normal distribution with a standard deviation of $40‚000. A. If we select a random sample of 50 households‚ what is the standard error of the mean? σ/√n =
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Continuous Distributions Distribution Uniform Normal Exponential Gamma Chi-square Beta Probability Function f (y) = f (y) = 1 ; θ ≤ y ≤ θ2 θ2 − θ1 1 1 1 (y − µ)2 √ exp − 2 2σ σ 2π −∞ < y < +∞ f (y) = 1 y α−1 e−y/β ; (α)β α 0<y<∞ f (y) = f (y) = f (y) = 1 −y/β e ; β>0 β 0<y<∞ (y)(v/2)−1 e−y/2 2v/2 (v/2) y2 > 0 ; (α + β) y α−1 (1 − y)β−1 ; (α) (β) 0<y<1 MomentGenerating Function Mean Variance θ1 + θ2 2 (θ2 − θ1 )2 12 µ σ2 β β2 (1 − βt)−1 αβ αβ 2 (1 − βt)−α v 2v
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| |Applications |In industries where large numbers of similar machines and workers engaged on similar tasks are employed. | |Underlying Principle |The theory of activity sampling is based on the laws of probability and binomial distribution. The concept| | |is that the characteristics of a large enough‚ yet unbiased sample chosen at random would be | | |representative of the population characteristics.
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MA 211 Item Bank Quiz 2: Chapters 7-9 Chapter 7 Multiple-Choice Questions 1. What does a hypothesis help you determine? a. Statisitcal techniques to be used b. Research question c. Average score d. Sampling error 2. Which of the following refers to the group to which you wish to generalize your results? e. Sample f. Population g. Sampling error population h. General group 3. What does “generalizability” mean? i. Results
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Chapter 5 1) An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight‚ but most of them had satisfactory weight. What is the probability of selecting three packages that are satisfactory? Answer: P(all 3 satisfactory) = (0.9) (0.9) (0.9) = 0.729 2) A study of interior designers ’ opinions with respect to the most desirable primary color for executive offices showed that: What is the probability
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tests‚ such as a “two sample T-test”‚ a “paired sample T-test” or a “two sample Z test.” In order for a one way Analysis of Variance F test to be conducted‚ the following conditions must be met: (1) Each sample must be selected from a normal‚ or approximately normal‚ population. (2) The samples must be independent and randomly selected. (3) Each population must have the same variance. Looking at the conditions stated above‚ all the samples provided by the Toronto Real Estate Board reflect data from
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pdf of the population distribution is 1 + αx −1 ≤ x ≤ 1 2 f (x|α) = ‚ −1 ≤ α ≤ 1‚ 0 otherwise and the method of moments estimate was found to be α ˆ = 3X (where X is the sample mean of the random sample X1 ‚ . . . ‚ Xn ). In this problem‚ you will consider the sampling distribution of α ˆ. (a) Show that the estimate α ˆ is unbiased. (b) Find Var[ˆ α]. [Hint: What is Var[X]?] (b) Use the central limit theorem to deduce a normal approximation to the sampling distribution of α ˆ . According to
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