Statistics for Business Economics – II — DU B.A. (Hons.) Business Economics (BBE) Previous Year Question Papers

Required statistical tables are attached with this paper. Find out the point estimator and estimate for determining the average performance of all students in the population. Also state the estimate you will use to separate the lowest 50% scoring students from the top 50%. Estimate its value. (c) A population consists of values {2, 4, 6) with probabilities 0.3, 0.4 and 0.3 respectively. (i) Construct the sampling distribution of sample mean for samples of size 2 drawn from the population with replacement. (ii) Compute the expected value of sample mean and compare it with the population mean. (111) Calculate the standard error of sample means. (a) The amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.2 minutes and standard deviation 1.5 minutes. Suppose that a random sample of n 49 customers is observed. Find the probability that the average time waiting in line for these customers is (1) Less than 10 minutes (ii) Between 5 and 10 minutes (b) The life in hours of a 75-watt light bulb is known to be normally distributed with standard deviation of 25 hours. A random sample of 20 bulbs has a mean life of 1014 (i) Construct a 92% two-sided confidence interval of the mean life. (ii) Construct a 90% lower-confidence bound of the mean. (iii) What sample size is needed if we want the width of the two-sided 95% confidence interval to be 6 hrs? (c) Consider a normal population distribution with the value of o known. What is the confidence level for the interval (x‡2.49o/Vn) and the upper bound (x+ (d) The sugar content of the syrup in canned peaches is normally distributed. A random sample of 10 cans yields a sample standard deviation of 4.8 milligrams. Find a 95% two-sided confidence interval for variance and standard deviation. (e) A sample of 15 observations is taken from a normally distributed population. The sample mean is found to be 52 and the sample standard deviation is 8. (i) Construct a 95% confidence interval for the population mean. (ii) How would the width of the confidence interval change if the sample size was increased to 25? Explain briefly. (f) You have been asked by the manager of an airport to evaluate which of two airlines does better in meeting their scheduled departure times. For each airline, you measure for 40 randomly selected flights: the time (in minutes) between scheduled departure and actual departure. You cannot assume that the populations of times are normally distributed or that there is homogeneity of variance. Your independent-sampling results are: airline (1) - X1 = 12.4 min, s1 = 3.72 min; airline (2) - X2 = 11.7 min, s2 = 3.60 min. What is the 99% confidence interval for M1 - M2? (a) The life in hours of a battery is known to be approximately normally distributed, with standard deviation 1.25 hours. A random sample of 10 batteries has a mean life of 40.5 (i) Is there enough evidence to support the claim that battery life exceeds 40 hours?