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Statistics (I) 2011Fal Quiz #1 Date: 10/13/2011 A. MULTIPLE CHOICE QUESTIONS (30%) 1. Temperature is an example of a variable that uses a. the ratio scale b. the interval scale c. the ordinal scale d. either the ratio or the ordinal scale 2. The nominal scale of measurement has the properties of the a. ordinal scale b. only interval scale c. ratio scale d. None of these alternatives is correct. 3. Statistical studies in which researchers control variables of interest are a. experimental studies b. control observational studies c. non-experimental studies d. observational studies 4. A statistics professor asked students in a class their ages. On the basis of this information, the professor states that the average age of all the students in the university is 24 years. This is an example of a. a census b. descriptive statistics c. an experiment d. statistical inference 5. Qualitative data can be graphically represented by using a(n) a. histogram b. frequency polygon c. ogive d. bar graph 1 6. 7. Since the population size is always larger than the sample size, then the sample statistic a. can never be larger than the population parameter b. c. d. can never be equal to the population parameter can be smaller, larger, or equal to the population parameter can never be smaller than the population parameter The value which has half of the observations above it and half the observations below it is called the a. b. c. range median mean d. mode 8. When data are positively skewed, the mean will usually be a. greater than the median b. smaller than the median c. equal to the median d. positive 9. The numerical value of the standard deviation can never be a. larger than the variance b. zero c. negative d. smaller than the variance 10. The value of the sum of the deviations from the mean, i.e., ( x x) must always be a. b. c. d. less than the zero negative either positive or negative depending on whether the mean is negative or positive zero 11. If the coefficient of variation is 40% and the mean is 70, then the variance is a. b. c. d. 28 2800 1.75 784 2 12. If a six sided die is tossed two times and “3” shows up both times, the probability of “3” on the third trial is a. much larger than any other outcome b. c. d. much smaller than any other outcome 1/6 1/216 13. If P(A) = 0.4, P(B| A) = 0.35, P(A B) =0.69, then P(B) = a. 0.14 b. 0.43 c. 0.75 d. 0.59 14. Two events with nonzero probabilities a. can be both mutually exclusive and independent b. can not be both mutually exclusive and independent c. are always mutually exclusive d. are always independent 15. If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(AB) = a. 0.05 b. 0.0325 c. 0.65 d. 0.8 3 B. Problems (70%) 1. (8%) A sample of twelve families was taken. Each family was asked how many times per week they dine in restaurants. 2 1 0 2 0 2 1 Their responses are given below. 2 0 2 1 2 Using this data set, compute the a. mode b. median c. mean d. range e. interquartile range f. variance g. standard deviation h. coefficient of variation 2. (8%) The following data represent the daily supply (y in thousands of units) and the unit price (x in dollars) for a product. Daily Supply (y) Unit Price (x) 5 2 7 4 9 8 12 5 10 13 16 16 a. b. c. d. 7 8 16 6 Compute and interpret the sample covariance for the above data. Compute the standard deviation for the daily supply. Compute the standard deviation for the unit price. Compute and interpret the sample correlation coefficient. 4 3. (8%) As a company manager for Claimstat Corporation there is a 0.40 probability that you will be promoted this year. There is a 0.72 probability that you will get a promotion or a raise. The probability of getting a promotion and a raise is 0.25. a. If you get a promotion, what is the probability that you will also get a raise? b. Are getting a raise and being promoted independent events? Explain using probabilities. c. Are these two events mutually exclusive? Explain using probabilities. d. Are these two events independent? Explain using probabilities. 4. (6%) Assume two events A and B are mutually exclusive and, furthermore, P(A) = 0.2 and P(B) = 0.4. a. Find P(A B). b. Find P(A B). c. Find P(AB). 5. (14%) A small town has 5,600 residents. The residents in the town were asked whether or not they favored building a new bridge across the river. You are given the following information on the residents' responses, broken down by sex. In Favor Opposed Total a. b. c. d. e. f. g. Men 1,400 840 2,240 Women 280 3,080 3,360 Total 1,680 3,920 5,600 Find the joint probability table. Find the marginal probabilities. What is the probability that a randomly selected resident is a man and is in favor of building the bridge? What is the probability that a randomly selected resident is a man? What is the probability that a randomly selected resident is in favor of building the bridge? What is the probability that a randomly selected resident is a man or in favor of building the bridge? A randomly selected resident turns out to be male. Compute the probability that he is in favor of building the bridge. 5 6. (8%) In a recent survey about appliance ownership, 58.3% of the respondents indicated that they own Maytag appliances, while 23.9% indicated they own both Maytag and GE appliances and 70.7% said they own at least one of the two appliances. Define the events as M = Owning a Maytag appliance G = Owning a GE appliance a. b. c. What is the probability that a respondent owns a GE appliance? Given that a respondent owns a Maytag appliance, what is the probability that the respondent also owns a GE appliance? Are events “M” and “G” mutually exclusive? Why or why not? Explain, using d. probabilities. Are the two events “M” and “G” independent? Explain, using probabilities. 7. (6%) What is the probability of drawing the 4 aces as the first 4 cards if 4 cards are drawn at random and without replacement from a deck of 52 playing cards? Please note that you are required to use conditional probability instead of counting rule. 8. (6%) In a factory of 4 machines producing the same product. Machine A, B, C, and D produces 10%, 20%, 30%, and 40% of products, respectively. The proportion of defective items produced by these machines follows 0.001 for machine A, 0.0005 for machine B, 0.005 for machine C, 0.002 for machine D. An item randomly selected is found to be defective. What is the probability that the item was produced by A? C? 9. (6%) The circuit shown below operates only if there is a path of functional devices from left to right. The probability that each device functions is shown on the graph. Assume that devices fail independently. What is the probability that the circuit operates? 6 0.9 0.95 0.9 0.99 0.95 0.9 7