According to the National Center for Health Statistics, the mean height of an American male is 69.3 inches and the mean height of an American female is 63.8 inches. The standard deviation for both genders is 2.7 inches. According to Chebyshev’s Theorem (look in the Guided Worksheets on page 49 for more information), what heights for your gender mark the 75% data values? If height is assumed to be normal what percentages lies between those two heights? Chebyschev’s Theorem: For any data set at least 75% of the data values are within 2 standard deviations of the mean and at least 89% are within 3 SD’s.
Part1 Q1. Classify each of the following as:- (i) qualitative or quantitative (ii) nominal, ordinal, interval or ratio scale. a.Times for swimmers to complete a 50meters race. b.Months of the year: Meskerem, Tikimit, Hidat, ---. c.Region numbers of Riyadh: 1, 2, 3, 4, ---. d.Pollen counts provided as numbers between 1 and 10 where 1 means there is almost no pollen and 10 means that it is rampant, but for which the values do not represent an actual count of grains of pollen. e. Packages in the city of Cleveland telephone book. f. Rankings of tennis players. g. Weights of air conditioners. h.Personal ID numbers i. Telephone numbers j. Temperatures inside 10 refrigerators. k.Salaries of the top five CEOs in the United States. l. Ratings of eight local plays ( poor, fair, good, excellent) m. Times required for mechanics to do a tune up. n. Ages of students in a classroom. o. Marital Status of patients in a physician’s office. p. Horsepower of tractor engines. q. Colors of baseball caps in a store. r.Classification of kids at a day care (infant, toddler, pre-school) Q2. The following are the grades which 40 students obtained in a certain course in 1997E.C. here in Mekelle University of the Arid Campus. 75 89 66 52 90 68 83 94 77 60 38 47 87 65 97 49 65 72 73 81 63 77 31 88 74 37 85 76 74 63 69 72 91 87 76 58 63 70 72 65 a. Construct an absolute frequency distribution. b. Convert the distribution obtained in (a) into a Relative & Percentage distribution. c. Convert the distribution in (a) into a “Less than” & a “More than” cumulative distribution d. Construct a histogram, frequency polygon and ogive curve Q3. The following distribution shows that the result obtained by 100 accounting students in the final examination of statistics in Saudi Electronic University. Mark of students. 0-10 10-20 20-30 30-40 40-50 No. of students 14 f1 28 f2 15 If the median mark of students is 22.5, compute:- i. The missing frequencies, f1 and f2. ii. the mode, and iii. the arithmetic mean iv. variance Part 2 Q1. a. (Smoking and Coffee Drinking) Coffee No Coffee Total Smoker 60 40 100 Non-Smoker 115 85 200 Total 175 125 300 What is the probability that a randomly selected person from the sample either smokes or drinks coffee. Q1. b. What is the probability that I flip a coin and get a Head, Roll a die and get a 4 or a 6, and then pull the king of Spades and a diamond from a deck of cards. Q2: The random variable X has the following probability distribution: X 0 1 2 3 Total P(x) 0.22 0.38 0.1 0.3 1 Find the expected value (E(x)) & the Variance. Q3: A radar unit is used to measure speeds of cars on a highway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random is travelling at: a- More than 100 km/hr? b- Less than 85 Km/hr? c- Between them? Part 3 Q-1. In a random sample consisting of 60 students of a college, 2 were smokers. In a random sample consisting of 17 lecturers of the college, 5 were smokers. Test at 5% level of significance that the proportion of smokers among the students is the same as that among lecturers. Q-2.The following data shows the score of 12 students for Accounting and Statistics examinations. a) Calculate a simple correlation coefficient b) Fit a regression equation of Statistics on Accounting using least square estimates. c) Predict the score of Statistics if the score of accounting is 85. Accounting X Statistics Y 1 74.00 81.00 2 93.00 86.00 3 55.00 67.00 4 41.00 35.00 5 23.00 30.00 6 92.00 100.00 7 64.00 55.00 8 40.00 52.00 9 71.00 76.00 10 33.00 24.00 11 30.00 48.00 12 71.00 87.00 Q3. Calculate the simple correlation between mid semester and final exam scores of 10 students (both out of 50) Student Mid Sem.Exam (X) Final Sem.Exam (Y) 1 31 31 2 23 29 3 41 34 4 32 35 5 29 25 6 33 35 7 28 33 8 31 42 9 31 31 10 33 34 Part 4 Q1. Random samples of 200 men, all retired were classified according to education and number of children is as shown below Education level Number of children 0-1 2-3 Over 3 Elementary 14 37 32 Secondary and above 31 59 27 Test the hypothesis that the size of the family is independent of the level of education attained by fathers. (Use 5% level of significance) Q2. Random sample of 180 staff from the whole workforce of the supermarket chain. Male Female Supervisor 20 15 Shelf stacker 20 30 Till operator 10 35 Cleaner 10 40 Test for association between a member of staff's job and his/her gender at the 5% significance level. Q3. One important factor in selecting software for word processing and database management systems is the time required to learn how to use a particular system. In order to evaluate three database management systems, a firm devised a test to see how many training hours were needed for five of its word processing operators to become proficient in each of three systems. System A 16 19 14 13 18 hours System B 16 17 13 12 17 hours System C 24 22 19 18 22 hours Using a 5% significance level, is there any difference between the training time needed for the three systems? PERCENTAGE POINTS OF THE F DISTRIBUTION a = 5% n1 n2 Numerator degrees of freedom 1 2 3 4 5 6 7 8 9 Denominator degrees of freedom 1 161.40 199.50 215.70 224.60 230.20 234.00 236.80 238.90 240.50 2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8081 4 7.71 6.94 6.56 6.39 6.26 6.16 6.09 6.04 6.00 5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 23 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22 30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 120 3.92 3.07 2.68 2.45 2.29 2.17 2.09 2.02 1.96 ¥ 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88
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