B.Sc. (Computer Science) Sem 2 October 2023 October 2023 Statistical Methods Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q4 | All questions are compulsory Figures to the right indicate full marks Use of non-programmable calculator is allowed Graph paper will be provided on request Attempt the following. (Any Four) (20) For the following probability distribution of X
   • a) Find value of k,
   • b) Find P(X = 3), P(X < 4),
   • c) Find probability distribution of Y = 2X - 1 Vijay has started new retail out let in mid of the market. In market there is business & competition. Therefore survival of a new outlet is very rare chance of survival is almost 5%. Vijay has started such 7 new retail outlet. Find out the | (05)
   • a) Atleast 3 shops will survive, b) Exactly 5 shops will survive
   • a) Discrete Random Variable with example, 3 b) Continuous Random Variable with example, (05)
   • c) Variance of Discrete Random Variable,
   • e) Binomial Distribution Let X be a continuous random variable whose probability density function is
   • a) c.d.f. of random variable, b) P(1<X< 2), c) P(1.5<X< 4) The mean & variance of a binomial variate are 12 & 6. Find (05) 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, i.e., what is P(X | (05) Attempt the following. (Any Four) (20)
2. Q1 | Areal estate agency wants to compare the price of two BHK flats in two areas of Bangalore City. Asample of 60 listings in Area 1 & 99 listings in Area 2 yields the following results (in lakhs of rupees) : At the 0.05 level of significance, is there evidence that the average price in area 1 is higher than area 2? The manufacturing of rubber chemicals by a batch process, has a normal yield of 690 Ibs per batch. A new process is tried experimentally on 12 batches with the following yields : (05) Is the yield of the new process a significantly different from that of the old process? (Level of significance is 0.01
3. Q3 | Astudy was conducted on the use of cell phones for accessing news. Suppose that the survey consisted of 1,000 users under age 50, of whom 470 accessed news on their cell phones, & 891 users age 50 & over, of whom 134 accessed news on their cell phones. Is there evidence that the proportion of users under (05) age 50 is more than users 50 years & older that accessed the news on their cell Suppose the State Government wants to examine the safety of compact cars, medium cars, & big cars. It collects a sample of three for each of the treatments (car types). Using the hypothetical data provided below, find Combined Mean What is Analysis of Variance? Explain the types of it. (05) A process is known to produce bricks whose weights are normally distributed with standard deviation 0.12 pounds. A random sample of sixty bricks from today’s output had a mean weight of 4.07 pounds. Find a 99% confidence | (05) interval for the mean weight of all bricks produced today. The value of Z for @ = 0.99 is 2.58 Attempt the following. (Any Four) (20) What is Mann-Whitney U Test? Write assumptions of it. (05) Following is the data related to supporting a particular party & geographical Check is there any association between supporting a particular political party &
4. Q3 What is non-parametric test? What are the situations when one need to use non What is the Wilcoxon Signed Rank Test? Is there a difference between the median value for the following sets of treatment data for the twelve groups? What is the Kruskal Wallis Test? Hence Interpret on the basis of Critical Chi Square Value & H Value from the following example A shoe company wants to know if three groups of workers have different What is Post hoc analysis? Write four different types of post hoc test. (05) following. (Any Three) (15) What is Critical Region & p-value approach in testing of hypothesis? (05) What is hypothesis? Distinguish between Null Hypothesis & Alternate (05) 5 marks
5. Q3 | Write the properties of Chi-Square Distribution. Differentiate between Parametric & Non Parametric Test. (05) State four properties of t-distribution Write three Characteristics of the t-distribution that differ from the normal | (05) Date: -09/10/2023 Total Marks: - 75 Time: -02.00 pm to 04.30 pm 5 marks
   • N.B. 1. All questions are compulsory
6. Q2 Figures to the right indicate full marks
7. Q3 Use of non-programmable calculator is allowed
8. Q4 Graph paper will be provided on request
   • Q. Attempt the following. (Any Four) The germination success rate for begonia seeds is 60%. In a package of 200 20
9. Q1 seeds, what is the probability that over half of them germinate, i.e., what is P(X Let X be a continuous random variable whose probability density function is 5 marks
   • a) c.d.f. of random variable, b) c) P(1.5<X< 4)
   • a) Discrete Random Variable with example, 3 b) Continuous Random Variable with example, (05)
   • c) Variance of Discrete Random Variable,
   • e) Binomial Distribution Vijay has started new retail out let in mid of the market. In market there is business & competition. Therefore survival of a new outlet is very rare chance
10. Q4 ofsurvival is almost 5%. Vijay has started such 7 new retail outlet. Find 5 marks
    • a) Atleast 3 shops will survive, b) Exactly 5 shops will survive 5 The mean & variance of a binomial variate are 12 & 6. Find (05) For the following probability distribution of X
    • a) Find value of k,
    • b) Find P(X = 3), P(X < 4),
    • c) Find probability distribution of Y = 2X - 1
11. Q11 Attempt the following. (Any Four) agency wants to compare the price of two BHK flats in two areas of Bangalore City. Asample of 60 listings in Area 1 & 99 listings in Area 2 yields the following results (in lakhs of rupees) : At the 0.05 level of significance, is there evidence that the average price in area 1 is higher than area 2? 20 marks
12. Q2 Suppose the State Government wants to examine the safety of compact cars, medium cars, & big cars. It collects a sample of three for each of the treatments (car types). Using the hypothetical data provided below, find Combined Mean
13. Q3 A process is known to produce bricks whose weights are normally distributed with standard deviation 0.12 pounds. A random sample of sixty bricks from today’s output had a mean weight of 4.07 pounds. Find a 99% confidence (05) interval for the mean weight of all bricks produced today. The value of Z for @ = 0.99 is 2.58 4, study was conducted on the use of cell phones for accessing news. Suppose that the survey consisted of 1,000 users under age 50, of whom 470 accessed news on their cell phones, & 891 users age 50 & over, of whom 134 accessed news on their cell phones. Is there evidence that the proportion of users under (05) age 50 is more than users 50 years & older that accessed the news on their cell
14. Q5 The manufacturing of rubber chemicals by a batch process, has a normal yield of 690 Ibs per batch. A new process is tried experimentally on 12 batches with the following yields : (05) Is the yield of the new process a significantly different from that of the old process? (Level of significance is 0.01) What is Analysis of Variance? Explain the types of it. (05)
15. Q11 I Attempt the following. (Any Four) 20 marks
16. Q1 non-parametric test? What are the situations when one need to use non
17. Q2 Following is the data related to supporting a particular party & geographical Check is there any association between supporting a particular political party &
18. Q3 Whatis the Wilcoxon Signed Rank Test? Is there a difference between the median value for the following sets of treatment data for the twelve groups?
19. Q4 What is Mann-Whitney U Test? Write assumptions of it. What is the Kruskal Wallis Test? Hence Interpret on the basis of Critical Chi Square Value & H Value from the following example A shoe company wants to know if three groups of workers have different What is Post hoc analysis? Write four different types of post hoc test. (05) 5 marks
    • Q.V Attempt the following. (Any Three) 1 What is hypothesis? Distinguish between Null Hypothesis & Alternate (05) 15
20. Q2 Differentiate between Parametric & Non Parametric Test. 5 marks
21. Q3 Write the properties of Chi-Square Distribution. State four properties of t-distribution 5 marks
22. Q4 Write three Characteristics of the t-distribution that differ from the normal 5 marks
23. Q5 Whatis Critical Region & p-value approach in testing of hypothesis? 5 marks

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