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ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD (Department of Statistics) WARNING 1. 2. PLAGIARISM OR HIRING OF GHOST WRITER(S) FOR SOLVING THE ASSIGNMENT(S) WILL DEBAR THE STUDENT FROM AWARD OF DEGREE/CERTIFICATE, IF FOUND AT ANY STAGE. SUBMITTING ASSIGNMENTS BORROWED OR STOLEN FROM OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN “AIOU PLAGIARISM POLICY”. Course: Statistics & Probability (3447) Level: Graduation Total Marks: 100 Semester: Autumn, 2016 Pass Marks: 50 ASSIGNMENT No. 1 Note: All questions carry equal marks. Q.1 a) b) Q.2 a) b) What is a statistical data? Distinguish the following: (10) i) Primary and secondary data ii) Qualitative and quantitative data iii) Discrete and continuous data Arrange the data given below in an array and construct a frequency distribution, using a class interval of 5.00. Indicate the class limits and class boundaries clearly. (10) 79.4, 71.6, 95.5, 73.0, 72.2, 81.8, 90.6, 55.9, 75.2, 81.9, 68.9, 74.2, 80.7, 65.7, 67.6, 82.9, 88.1, 77.8, 69.4, 83.2, 82.7, 73.8, 64.2, 63.9, 58.3, 48.6, 83.5, 70.8, 72.1, 71.6, 59.4, 77.6. Describe the properties of standard deviation. Explain standard coefficient of dispersion. (10) The following frequency distribution shows the marks in a test of 100 students. (10) Marks Number of students 30–39 10 40–49 14 50–59 26 60–69 20 70–79 18 80–89 12 Calculate the mean, median, mode and standard deviation. Also interpret the results. Q.3 a) Explain what is meant by random experiment? Define sample space, random event, complementary events, equally likely events and exhaustive events. (10) 1 b) A marble is drawn from a box containing 10 red, 15 black, 5 green and 10 yellow marbles. Find the probability that the marble is (i) black (ii) not green or yellow (iii) red or black or green (iv) not blue. (10) Q.4 a) What is meant by (i) binomial experiments (ii) binomial random variable and binomial probability mass function? (10) The incidence of occupational disease in an industry is such that the workmen have a 20% chance of suffering from it? What is the probability that out of 6 workmen, (i) not more than 2 (ii) 4 or more will catch the disease. (10) b) Q.5 a) b) Differentiate between parameter and statistics. Explain the advantages of sampling. (10) Draw all possible samples of size 2 without replacement from a population consisting of 4, 7, 8, 12, and 18. From the sample distribution of sample means and verify the results. (10) ASSIGNMENT No. 2 Total Marks: 100 Pass Marks: 50 Note: All questions carry equal marks. Q.1 a) b) Q.2 a) b) Explain in detail the procedure of testing a null hypothesis with suitable example. (10) For a sample of 60 women taken from a population of over 5,000 enrolled in a weight-reducing program a nationwide chain of health spas, the sample mean diastolic blood pressure is 101 and the sample standard deviation is 42. At a significance level of 0.02 on the average, did the women enrolled in the program have diastolic blood pressure that exceeds the value of 75? (10) Explain with examples the difference between: (10) i) Simple Hypothesis and Composite Hypothesis ii) Acceptance Region and Rejection Region iii) Statistic and Test Statistic iv) Type-I Error and Type-II Error Consider the case of pharmaceutical manufacturing company testing two now compound indenting to reduce bold pressure levels. The compound is administered to two different sets of laboratory animals. Group one, 71 of 100 animals testing respond to drug one with lower bold pressure levels. In group two 50 of 90 animals testing respond to drugs two lower blood pressure level the company want to test at the 5% level whether there is a 2 different between the efficacies of these two drugs. How should proceed these drugs. (10) Q.3 a) b) Define and explain the terms regression and correlation. Describe the properties of least square regression line. (10) The following sample of 8 grade point averages and marks in matriculation was observed for students from a college. (10) Score GPA 480 2.7 490 2.9 510 3.3 510 2.9 530 3.1 550 3.0 610 3.2 640 3.7 Fit Y = a + βX + ε by least squares method and estimate the mean GPA of students scoring 600 marks. Q.4 a) b) What is meant by a random variable? Differentiate between the discrete random variable and continuous random variable. (10) At the 0.10 level of significance, can we concluded that the following 400 observations follow a Poisson distribution with λ = 3? (10) 0 20 Number of arrivals per hour Number of hours Q.5 a) b) 1 57 2 98 3 85 4 78 5 or more 62 What is meant by analysis of variance? Explain the general procedure for it. (10) Three training methods were compared to see whether they led to greater productivity after training. The following are the productivity measures for individual trained by each method. (10) Method 1 Method 2 Method 3 45 59 41 40 43 37 50 47 43 39 51 40 53 39 52 44 49 37 At the 0.05 level of significance, do the three training methods lead to different levels of productivity? 3