# stat

Part1Q1. 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 numbersi.  Telephone numbersj.   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  65a. 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 distributiond. Construct a histogram, frequency polygon and ogive curveQ3. 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.0-1010-2020-3030-4040-50No. of students14f128f215If the median mark of students is 22.5, compute:-i.     The missing frequencies, f1 and f2.ii.     the mode, andiii.     the arithmetic meaniv.     variancePart 2Q1.  a. (Smoking and Coffee Drinking)CoffeeNo CoffeeTotalSmoker6040100Non-Smoker11585200Total175125300What 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:X0123TotalP(x)0.220.380.10.31Find 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 3Q-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 Statisticsexaminations.a)     Calculate a simple correlation coefficientb)    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.AccountingXStatisticsY174.0081.00293.0086.00355.0067.00441.0035.00523.0030.00692.00100.00764.0055.00840.0052.00971.0076.001033.0024.001130.0048.001271.0087.00Q3. Calculate the simple correlation between mid semester and final exam scores of 10 students (both out of 50)StudentMid Sem.Exam(X)Final Sem.Exam(Y)131312232934134432355292563335728338314293131103334Part 4Q1. Random samples of 200 men, all retired were classified according to education and number of children is as shown belowEducation levelNumber of children0-12-3Over 3Elementary143732Secondary and above315927Test 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.MaleFemaleSupervisor2015Shelf stacker2030Till operator1035Cleaner1040Test 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    hoursSystem B     16      17      13      12      17    hoursSystem C     24      22      19      18      22    hoursUsing 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%n1n2Numerator degrees of freedom123456789Denominator degrees of freedom1161.40199.50215.70224.60230.20234.00236.80238.90240.50218.5119.0019.1619.2519.3019.3319.3519.3719.38310.139.559.289.129.018.948.898.85808147.716.946.566.396.266.166.096.046.0056.615.795.415.195.054.954.884.824.7765.995.144.764.534.394.284.214.154.1075.594.744.354.123.973.873.793.733.6885.324.464.073.843.693.583.503.443.3995.124.263.863.633.483.373.293.233.18104.964.103.713.483.333.223.143.073.02114.843.983.593.363.203.093.012.952.90124.753.893.493.263.113.002.912.852.80134.673.813.413.183.032.922.832.772.71144.603.743.343.112.962.852.762.702.65154.543.683.293.062.902.792.712.642.59164.493.633.243.012.852.742.662.592.54174.453.593.202.962.812.702.612.552.49184.413.553.162.932.772.662.582.512.46194.383.523.132.902.742.632.542.482.42204.353.493.102.872.712.602.512.452.39214.323.473.072.842.682.572.492.422.37224.303.443.052.822.662.552.462.402.34234.283.423.032.802.642.532.442.372.32244.263.403.012.782.622.512.422.362.30254.243.392.992.762.602.492.402.342.28264.233.372.982.742.592.472.392.322.27274.213.352.962.732.572.462.372.312.25284.203.342.952.712.562.452.362.292.24294.183.332.932.702.552.432.352.282.22304.173.322.922.692.532.422.332.272.21404.083.232.842.612.452.342.252.182.12604.003.152.762.532.372.252.172.102.041203.923.072.682.452.292.172.092.021.96¥3.843.002.602.372.212.102.011.941.88