IGNOU BCS-40 - Statistical Techniques

Q1. Calculate the mean and standard deviation for the following data: Q2. Given the following sample of 20 numbers: 15 45 52 43 50 59 41 47 56 79 72 18 45 54 78 12 41 48 58 14 (i) Compute mean, variance and standard deviation. (ii) If the largest value in the above set of numbers is changed to 500, to what extent are the mean and variance affected by the change? Justify your answer. Q3. (a) Write two merits and two demerits of Median. (b) An incomplete frequency distribution is given as follows 12 30 ? 65 ? 25 18 Given that median value of 200 observations is 46, determine the missing frequencies using the median formula. Q4. Box X contains 5 red and 4 blue balls, Box Y contains 2 red and 5 blue balls. A ball is drawn at random from each box. Find the probability of drawing one red and one blue ball. Q5. A Manager of a car company wants to estimate the relationship between age of cars and annual maintenance cost. The following data from six cars of same model are obtained as: (a) Construct a scatter diagram for the data given above. (b) Fit a best linear regression line, by considering annual maintenance cost as the dependent variable and the age of the car as the independent variable. (c) Use this regression line to predict the annual maintenance cost for the car of age 8 years. Q6. Suppose A and B are two independent events, associated with a random experiment. If the probability of occurrence of either A or B equals 0.6; while probability that only A occurs equals 0.4, then determine the probability of occurrence of event B. Q7. A chemical firm wants to determine how four catalysts differ in yield. The firm runs the experiment in three of its plants, types A, B, C. In each plant, the yield is measured with each catalyst. The yield (in quintals) are as follows: (a) Perform an ANOVA and comment whether the yield due to a particular catalyst is significant or not at 5% level of significance. Given F 3,6= 4.76. (b) Construct ANOVA table for one-way classification. Q8. Explain the following with the help of an example each: a) Binomial distribution b) t-test for mean c) Properties of good estimator d) F-test for Equality of two variances

Q1. In a study on the Per capita Income for a particular year in a city, the following weekly observations were made. Draw a histogram and a frequency polygon on the same scale Q2. Do you find any correlation between ages and playing habits of the students, whose distribution according to age groups is given in the following table Q3. Data are given below shows statistics viz. standard deviation & average marks secured by students, in the examination of subject A and B Assuming the Coefficient of correlation between A and B = ±0.66 Perform the following tasks: i) Determine the two equations of regression ii) Calculate the expected marks in A corresponding to 75 marks obtained in B. Q4. Calculate 2-sigma and 3-sigma upper and lower control limits for means of samples 4 and prepare a control chart for a drilling machine, which bores holes with a mean deviation of 0.5230 cm and a standard deviation of 0.0032 cm. Q5. Construct 5- yearly moving averages from the following data Q6. In 120 throws of a single dice, following distribution of faces was observed. From the given data, verify that the hypothesis “dice is biased” is acceptable or not. Q7. A company wants to estimate, how its monthly costs are related to its monthly output rate. The data for a sample of nine months is tabulated below: Using the data given above, perform following tasks: (a) Calculate the best linear regression, where the monthly output is the dependent variable and monthly cost is the independent variable. (b) Use the regression line to predict the company’s monthly cost, if they decide to produce 4 tons per month. Q8. The Probability that at least one of the two Independent events occur is 0.5. Probability that 5 first event occurs but not the second is (3/25). Also the probability that the second event occurs but not the first is (8/25). Find the probability that none of the two event occurs. Q9. Marks of six students are tabulated below : From the population, tabulated above, you are suppose to choose a sample of size two. (a) Determine, how many samples of size two are possible (b) Construct sampling distribution of means by taking samples of size 2 and organize the data. Q10. Two new types of petrol, called premium and super, are introduced in the market, and their manufacturers claim that they give extra mileage. Following data were obtained on extra mileage which is defined as actual mileage minus 10. (i) Using ANOVA, test whether premium or super gives an extra mileage. (ii) What is your estimate for the error variance? (iii) Assuming that the error variance is known and is equal to 1, obtain the 95 % confidence interval for the mean extra mileage of super. Q11. Two floppies are selected at random without replacement from a box containing 7 good and 3 defective floppies. Let A be the event that the first floppy drawn is defective, and let B be the event that the second floppy drawn is defective. (i) Find the conditional probabilities P(B/A) and P(B/AC) (ii) Show that P(B) = P(B/A). P(A) + P(B/AC) P(AC) = P(A). Q12. A drilling machine bores holes with a mean deviation of 0.5230 cm and a standard deviation of 0.0032 cm. Calculate 2-sigma and 3-sigma upper and lower control limits for means of samples 4 and prepare a control chart. Q13. What are control charts briefly discuss the utility of control charts? Q14. Compare the following a) Cluster sampling , Stratifies sampling and Systematic sampling b) Parametric and Non-Parametric Tests Q15. Explain the following with the help of an example each: a) Goodness of fit test b) Test of Independence c) Criteria for a good estimator d) Chi-Square Test