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Economics 310: Economic Statistics Quick Review for Exam 1, part b Exam 1, part b covers chapter 2, 3 and class notes. Complete the following exercises for a cursory review of the concepts that you will be tested upon on this exam. These questions are not a substitute for the assigned homework nor should they be construed as a study guide! Merely stating answers to calculations is insufficient to receive complete credit. Calculators may be used to aid in your calculations but formulas and set up of mathematical problem must be shown to receive full credit. Finally, one 8 ½” X 11” sheet of paper may be used as a formula card with any formulas or notes that you wish to write on both sides. 1. True or false: the average (mean) age of people who respond to a particular survey is an example of a parameter. 2. The first two classes of a frequency distribution are 0 – 9 and 10 – 19. What is the class length? 3. The first two classes of a frequency distribution are 0 – 9 and 10 – 19. What are the class boundaries of the first class? 4. Can the original 27 values of a data set be identified by knowing that 27 is the frequency for the class 0 – 9? Why or why not? 5. True or false: When a die is rolled 600 times, each of the 6 possible outcomes occurs about 100 times as we normally expect, so the frequency distribution summarizing the results is an example of a normal distribution. Explain and elaborate your answer. 6. Fill in the blank: For typical data sets, it is important to investigate center, types of distribution, ___________ and outliers. 7. What values are represented by this stem and leaf diagram? 5 | 2 2 9 8. Which graph is best for paired data consisting of shoe sizes and heights of 30 randomly selected students: histogram, dotplot, scatterplot, pie chart? Explain and elaborate your answer. 9. True or false: A histogram and a relative frequency histogram constructed from the same data always have the same basic shape, but the vertical scales are different. 10. What characteristic of a data set can be better understood by constructing a histogram? Professor Camarena Bowerman Text, 4th edition 11. Construct a dotplot of the pulse rates of males listed in the following table. 68 72 56 88 64 56 64 56 88 68 60 64 72 64 64 56 64 60 84 56 72 68 76 60 60 60 84 64 88 60 88 72 76 56 96 72 60 84 72 84 12. When we compute the sample mean and standard deviation for the pulse rates of males we find that x is 69.4 and s=11.29738. Compute each of the intervals [x ± s], [x ± 2s], [x ± 3s]. Then count the number of pulse rates that actually fall into each interval and find the percentage of pulse rates that fall into each interval. 13. How do the percentages of the pulse rates that fall into the intervals [x ± s], [x ± 2s], [x ± 3s] compare to those given by the Empirical Rule? How do the percentages of the pulse rates that fall into the intervals [x ± 2s] and [x ± 3s] compare to those given by Chebyshev’s Theorem? 14. What is the mean of the sample values 2 cm., 2 cm., 3 cm., 5 cm, and 8 cm.? 15. What is the median of the sample values listed in question 14? 16. What is the mode of the sample values listed in question 14? 17. If the standard deviation of a data set is 5.0 feet, what is the variance of the data set? 18. If a data set has a mean of 10.0 seconds and a standard deviation of 2.0 seconds, what is the z score corresponding to the time of 4.0 seconds? 19. Fill in the blank: The range, standard deviation, and variance are all measures of ________ for a data set. 20. What is the symbol used to denote the standard deviation of a sample, and what is the symbol used to denote the standard deviation of a population? 21. What is the symbol used to denote the mean of a sample and what is the symbol used to denote the mean of a population? 22. Fill in the blank: Approximately ____ percent of values in a sample are greater than or equal to the 25th percentile. 23. True or false: For any data set, the median is always equal to the 50th percentile. Professor Camarena Bowerman Text, 4th edition Economics 310: Economic Statistics Quick Review for Exam 1, part b Answer Key 1. False. The mean age of people who respond to a survey is a sample statistic. Survey data cannot yield population parameters. 2. Ten as each of the numbers of the class boundaries are included in the class. As such, there are ten numbers between 0 and 9. 3. 0.5 and 9.5 4. Yes. Knowing that the first class of the table has a frequency equal to 27 indicates that all of the data values in the data set have been accounted for. The true question then becomes, why did all of the data values fall into the first class? Additional analysis must be done to determine if the class width is appropriate given the data set. 5. False. A normal distribution is characterized by frequencies that start low, peak in the middle, and end low. A symmetric or bell shaped curve can be expected. In this scenario, a uniform distribution is obtained. A uniform distribution occurs when each class’ frequency is identical. A histogram with a uniform distribution looks like this. 6. Changes in patterns of data over time, dispersion, or any other answer you can think of that accurately finishes this statement. 7. 52, 52, 59 8. Scatterplot. A scatterplot shows the relationship between two variables. All of the other graphs listed as answer choices are limited to showing data from only one variable. 9. True 10. The underlying distribution of the data set. A histogram is used to construct the underlying “curve” that the data fall in. The dispersion of the data as well as outliers can also be identified with a histogram. A histogram is also a good gauge for the data set’s place of center. Professor Camarena Bowerman Text, 4th edition 11. 12. Percen Number of t of observations Total 1 standard deviation 2 standard deviations 3 standard deviations 58.10262 to 80.69738 25 62.50% 46.80524 to 91.99476 39 97.50% to 103.2921 4 40 100% 35.50786 13. The empirical rule states that approximately 68% of all observations will fall within one standard deviation; 95% of all observations will fall within two standard deviations and 100% of all data observations will fall within three standard deviations. Chebyshev’s theorem states that at least (1-1/z2) of the data values must fall within z standard deviations of the mean, where z is any value greater than 1. Chebyshev’s Theorem cannot predict percentages of data within one standard deviation. Chevyshev’s Theorem does predict that at least 75% of the data must be within two standard deviations of the mean, 80% of the data must lie within three standard deviations of the mean, and 94% of the data must lie within four standard deviations from the mean. Comparing these two rules to the actual data observed, it can be seen that distribution of the pulse rates of males most closely resembles the expectations outlined by the empirical rule. 14. 4 cm. 15. 3 cm. 16. 2 cm. 17. Variance = 25.0 feet 18. Z = -3.00 19. Dispersion 20. Sample = s, population = σ 21. Sample = x , population = μ 22. 75% 23. True Professor Camarena Bowerman Text, 4th edition