B.Sc. (Computer Science) Sem 2 Statistical Methods Apr 2024 Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 All questions are compulsory
2. Q2 Mixing of sub questions is not
3. Q3 Write in clear, legible, writing Attempt any four: (20)
   • A) The following is cumulative distribution function of a discrete random
   • B) Let X be continuous random variable with
   • C) Write the properties of Chi square distribution
   • D) The germination success rate for begonia seeds is 60%. In a package of 200 seeds, what is the probability that over half of them germinate, what is P(X > 100)?
   • E) Write the properties of F distribution
   • F) The lion population in Gir National park is approximately distributed with mean # = 4400 lion and standard deviation 620 lion. Convert each of the following x intervals toz intervals and find the associated
   • a) more than 3300 b}lessthan 5400 between 3500 and 5300
4. Q2 Attempt any four: 20 marks
   • A) Acompany that manufactures chocolate bars is particularly concerned that the mean weight of a chocolate bar not be greater than 100 gm ounces. Past experience allows you to assume that the standard deviation ts 5 gm. A sample of 60 chocolate bars is selected, and the sample mean is 102 em. Using the 0.01 level of significance, is there evidence that the population mean weight of the chocolate bars is greater 100 gm. = 2.33)
   • B) Aprocess is known to produce bricks whose weights are normally distributed with standard deviation 0.12 pounds. Arandom sample of sixty bricks fram today's output had a mean weight of 4.07 pounds. Find a 99% confidence interval for the mean weight of all bricks produced today
   • C) The manufacturing of rubber chemicals by a batch process, has a normal yield of 690 lbs per batch Anew process is tried experimentally on 12 batches with the following yields: 620, 590, 660, 719, 690, 720, 700, 690, 720 and 650 Ibs. is the yield of the new process a significantly different from that of the old process? (Level of significance is 0.01) 106)
   • D) You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process in an to reduce the mean time between the order and completion of delivery from the current 25 minutes. From past experience, you can assume that the population standard deviation is 6 minutes. A sample of 36 orders using the new delivery process yields a mean of 22.4 minutes. At the 0.05 level of significance, is there evidence that the ponutation mean delivery time has been reduced below the previous population mean value of 25 minutes? = 1.64)
   • E) estate agency wants to compare the price of two BHK flats in two areas of Bangalore City. A sample of 60 listings in Area 1 and 99 listings in Area 2 yields the following results {in lakhs of At the level of significance, ts there is evidence that the average price in area higher
   • F) The helght of six randomly chosen soldiers are in inches: 63,65,68,65,71, and 72. Those of Set 10 chosen are Is there evidence that soldiers are taller than at 10% level of significance? ( = 1.76)
5. Q3 Attempt any four: 20 marks
   • A) Asmall scale manufacturing company want to know the effect af new machinery installed on defects produced In a A of n machines were chosen including new and old machines. Quality control managers were ask to recard the defects per lot The data are is there is any difference in defects produced by old and new machines. (hint:
   • B) Following Is the data related to supporting a particular party and geographical area Check is there any association between supporting a particular politica! party and area. A study is undertaken to know the impact of proper exercise on blood pressure of a teen age student, Total of 15 students were selected and blood recorded before the commencement of exercise program. Then a proper exercise following is the data related to attendance in a class. Use chi square test to know is there any association between Gender and Absenteeism
   • D) Anew skill based education is proposed to enhance ability of at graduate level. Professors are concerned with student's ability to employability and assess their marks before and after receiving tne new treatment 1=poor,2=fair,3=good,4=Ver; good, 5= excellent. The data are shown below (use Sign test, r at L.O.S is 2}
   • E) Explain Mann Whitney U test undertaken to know the impact of proper exercise on pressure of a teen age student, Total of 1S students were selected and blood pressure recorded before the commencement of exercise program. Then a proper exercise program was given to these students and again blood pressure was measured after completion of program. Following are the reading. (Hint: Wilcoxon signed rank
6. Q4 Attempt any five: 15 marks
   • A) Let X denotes the number of computers sold, and suppose that the pmf of X is 0.1; P{X=1)= 0.2; P(X=2)=0.3; find mean and variance,
   • B) Determine K such that the following are For X=0,1,2,3
   • C) Suppose that we wanted to calculate the 99% contidence level of the mean weight of bricks where ,S = 2.3, and size was 25. = 1.71909)
   • D) A professor in the accounting department of business claims that there is much more variability in final exam scores of students taking the introductary accounting course whe are not majoring in accounting. samples of 13 non accounting majors and 10 accounting majors are taken from the professor's class roster in his large lecture, and the following results are computed based on the exam scores: At the 5% level of significance is there is evidence to support claim?( Fre =
   • E) What is sign test?
   • F) Differentiate between parametric and non-parametric test

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