IGNOU BCS-40 - Statistical Techniques

Q1. In a partially destroyed laboratory, the legible record of analysis of correlation of data, is as follows: 10 Variance of x = 9, Regression equations: (10 Marks) i) 8x – 10y + 66 = 0 ii) 4x – 18y – 214 = 0 What were (a) the means of x and y, (b) the coefficient of correlation between x and y and (c) the standard deviation of y? Q2. A) A random sample of size 64 has been drawn from a population with standard deviation 20. The mean of the sample is 80. (i) Calculate 95% confidence limits for the population mean. (ii) How does the width of the confidence interval change if the sample size is 256 instead? B) A population consists of the numbers 2, 5, 7, 8 and 10. Write all possible simple random samples of size 3 (without replacement). Verify that the sample mean is an unbiased estimator of the population mean. Q3. A computer chip manufacturer claims that at most 2% of the chips it produces are defective. To check the claim of the manufacturer, a researcher selects a sample of 250 of these chips. If there are eight defective chips among these 250, test the null hypothesis that more than 2% of the chips are defective at 5% level of significance. Does this disprove the manufacturer's claim? (Given that Z0.05 = 1.645) Q4. A) A problem of statistics is given to three students A, B and C whose chances of solving it are 0.3, 0.5 and 0.6 respectively. What is the probability that the problem will be solved? B) Suppose 2% of the items made in a factory are defective. Find the probability that there are: (i) 3 defectives in a sample of 100 (ii) no defectives in a sample of 50 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. What do you understand by the term forecasting? With the help of a suitable example discuss the relation between forecasting and future planning. Briefly discuss both forecasting model. Q7. Using the Regression line y =90 + 50x, fill up the values in the table below. After filling the table, compute the parameters of Goodness to fit i.e. R and R2. Based on the result of R and R2, interpret the correlation between variable x and y. Q8. Explain the following with the help of an example each: (a) Linear and circular systematic sampling (b) Z-test and t-test (c) Correlation and Regression (d) Probability Distribution

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