GM03 Business Statistics Assignment - I Last Date of Submission: 15th October 2014 Maximum Marks: 100 Assignment Code: 2014GM03B1 Attempt all the questions. All the questions are compulsory and carry equal marks. Section-A 1. Prof. Hardtack gave four Friday quizzes last semester in his 10-student senior tax accounting class as follows: Quiz 1 Quiz 2 Quiz 3 Quiz 4 60 65 66 10 60 65 67 49 60 65 70 70 60 65 71 80 71 70 72 85 73 74 72 88 74 79 74 90 75 79 74 93 88 79 95 97 99 79 99 98 a) Find the mean, median, mode for each quiz. b) Based on the results obtained in (a) above, indicate the measure of central tendency you would like to use for each of the quizzes with reasons. 2. A biometric security devise using fingerprints erroneously refuses to admit 1 in 1000 authorized persons from a facility containing classified information. The device will erroneously admit 1 in 10,00,000 unauthorized persons. Assume that 95% of those who seek access are authorized. If the alarm goes off and a person is refused admission, what is the probability that really authorized? 3. Suppose the waiting time to get food after placing an order at a fast-food restaurant is exponentially distributed with a mean of 60 seconds. If a randomly selected customer orders food at the restaurant, what is the probability that the customer will have to wait at least two minutes? 4. A family has two children – one male child and the other a female child. Both the children are grown up and their daily expenditure is believed to be normally distributed with a mean of Rs.80 and Rs.60 for the male and the female child with standard deviation of Rs.20 and Rs.10 respectively. Find the probability that the two child together have an expenditure of more than Rs. 160. GM03/July 2014 Page 1/5 Section-B Case Study A car manufacturer who is producing cars at the rate of 4000 cars a month requires to procure ignition equipment from vendors. The company has a policy of placing orders for 12000 ignition equipment every time they order. The vendor has indicated that 3 % of the ignition equipment is likely to be faulty in each shipment. Since it is not possible to test each and every ignition equipment by the car manufacturer, the manufacturer decides to randomly sample 200 ignition equipment and if more than 2 of them are found to be defective the entire batch of order shall be returned back. Case Questions: a) What sampling method would you suggest for the car manufacturer? b) What is the probability that the batch will be returned back to the vendor. GM03/July 2014 Page 2/5 GM03 Business Statistics Assignment - II Assignment Code: 2014GM03B2 Last Date of Submission: 15th November 2014 Maximum Marks: 100 Attempt all the questions. All the questions are compulsory and carry equal marks. Section-A 1. Last year television stations WXYZ’s share of the 11pm news audience was approximately equal to 25%. The station’s management believes that the current audience share is higher than last years 25% figure. In an attempt to substantiate this belief, the station surveyed 400 11pm viewers and found that 146 watched WXYZ. Set up the null and alternative hypothesis and test the same at 5% level of significance. What is your conclusion? 2. A retailer that sells home entertainment systems accumulated 10451 sales invoices during the previous year. The total of the sales amount on these invoices as claimed by the company is Rs.63,84,675. In order to estimate the true total sales for last year, an independent auditor randomly selects 350 of the invoices and determines the actual sales amounts by contacting the purchasers. The mean and standard deviation of the 350 samples sales amounts are Rs. 532 and standard deviation 168. Find the point and interval estimate given that a 95% confidence is required. Do you think that the sales invoice claimed by the company are correct? 3. One of the questions on the Business Week subscriber study was, “In the past 12 months when travelling for business, what type of airline ticket did you purchase most often”. The data obtained are shown in the following table. Type of Flight Type of Ticket Domestic flights International flights First Class 29 22 Business / Executive class 95 121 Full fare economy /coach class 518 135 Based on the above can it be concluded that type of ticket is dependent on the type of flight taken. Use 5% level of significance. GM03/July 2014 Page 3/5 4. To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow. Construct an analysis of variance table. Use a 5% level of significance to test whether the temperature level has an effect on the mean yield of the process. Yield Temperature 50degC 34 24 36 39 32 60degC 30 31 34 23 27 70degC 23 28 28 30 31 SECTION-B Case Study A research project was undertaken to determine if there is a relationship between the years of experience on the job (A) and efficiency rating of employees (B). The objective of the study was to predict the efficiency rating of the employee. The sample results are as follows: Years of Job (A) 1 20 6 8 2 1 14 8 4 6 Efficiency rating (B) 6 5 3 5 2 2 4 3 3 4 a) Which variable is the dependent variable? b) Find if there is correlation between the two variables and test the correlation coefficient. (use 5% level of type I error) c) Estimate the linear regression model. Do you think that the regression coefficient would be significant at 5% level of significance? Give reasons. d) Do you think the overall regression model would be significant? Give reasons. GM03/July 2014 Page 4/5