------o0o------ CHAPTER 14: CHI-SQUARE TESTING STATISTICS FOR BUSINESS TAs: Vo Vuong Van Anh‚ Le Phuoc Thien Thanh‚ and Le Nhat Ho December 21‚ 2013 TABLE OF CONTENTS • PART I: CHI-SQUARE TESTING FOR GOODNESS-OF-FIT. • PART II: CHI-SQUARE TESTING FOR NORMAL DISTRIBUTION. • PART III: CHI-SQUARE TESTING FOR INDEPENDENCE. December 2013 Powered by Vo Vuong Van Anh 2 1 12/21/2013 Hypothesis Testing Procedure for Chi-Square Testing 5 Steps to Perform an Chi-Square Testing STEP 01 State the null and alternative
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The Cumulative Distribution Function. The uniform distribution is introduced. 3.4 The Normal Distribution General definition of this distribution. Properties of normal distribution Presentation of several examples of normal random variables and variables with non-normal distributions. 3.5 Computing Probabilities for the Normal Distribution 3.6 Sums
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specific distribution. The Kolmogorov-Smirnov (K-S) test is based on the empirical distribution function (ECDF). Given N ordereddata points Y1‚ Y2‚ ...‚ YN‚ the ECDF is defined as \[ E_{N} = n(i)/N \] where n(i) is the number of points less than Yi and the Yiare ordered from smallest to largest value. This is a step function that increases by 1/N at the value of each ordered data point. The graph below is a plot of the empirical distribution function with a normal cumulative distribution function
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Practice 1. When raw scores from normal distribution are converted to standard scores‚ the resulting distribution has a mean equal to ________ and SD equal to _________. 2. Scores on a particular test are normally distributed with a mean of 70 and an SD of 15. Between what two scores would you expect? a. 68% of the scores to fall between ____________ and _____________? b. 95% of the scores to fall between ____________ and _____________? 3. A distribution of scores has a mean of 70 and an
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1. Use the sales forecaster’s predication to describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its mean and standard deviation. Let’s assume that the expected sales distribution is normally distributed‚ with a mean of 20‚000‚ and 95% falling within 10‚000 and 20‚000. We know that +/- 1.96 standard deviations from the mean will contain 95% of the values. So‚ we can get the standard deviation by: z = (x -
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DIV1 P P 0 0 1 P P P 0 0 0 (2) PROBABILITY DISTRIBUTION AND EXPECTED RATE OF RETURN: E(R)=∑(i=1 to n)=p(i) *R(i)‚ where‚ E(R)=expected return‚ n=number of possible outcomes‚ p(i)=probability associated with R(i)‚ R(i)=return for the ith possible outcome. (3)Standard Deviation of Return: Risk refers to the dispersion of a variable. It is commonly measured by the variance or the standard deviation. The variance of a probability distribution is the sum of the squares of the deviations of actual
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secretaries‚ 20 technicians‚ 4 engineers‚ 2 executives‚ and 50 factory workers. If a person is selected at random‚ what is the probability that he or she is a factory worker? A) 1 4 B) 1 8 C) 5 8 D) 2 5 An apartment building has the following distribution of apartments: 1 bedroom 2 bedroom 1st floor 3 1 2nd floor 2 2 3rd floor 1 4 3 bedroom 1 2 1 If an apartment is selected at random‚ what is the probability that it is on the 2nd floor or has 2 bedrooms? A) 7 11 B) 6 11 C) 13 17 D) 11 17
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Statistics Midterm Review Name ____________________________ The next three questions concern the following scenario: A recent Gallup poll asked "Do you consider pro wrestling to be a sport‚ or not?" Of the people asked‚ 81% said "No." The results were based on telephone interviews with a randomly selected national sample of 1‚028 adults‚ 18 years and older‚ conducted August 16-18‚ 1999. 1. The population for this poll appears to be: (a) all professional wrestlers. (b) all adults
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(1) A study of the number of cars sold looked at the number of cars sold at 500 Dealers The smallest dealer had 11 cars sold and the largest had 154 cars sold. If you were going to create a frequency distribution of the number of cars sold using six classes in your frequency distribution‚ which of the following might be a reasonable first class? (a) 0 to 25 _ (2) Give that a sample of 25 had x =
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requirements of a normal distribution. If the ratios are normally distributed then parametric statistics should be used and if they are not then a non parametric statistics should be used (2008). However‚ in order to determine if a sample or any group of data fits a standard normal distribution‚ the histogram and the Normal Probability Plot are the simplest ways to check whether or not it is reasonable to assume that the random errors inherent in the process have been drawn from a normal distribution. Referring
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