Advanced Statistical Methods, Semester 3(2020-23), Feb 2022

SAINTGITS COLLEGE OF APPLIED SCIENCES

          PATHAMUTTOM, KOTTAYAM

 

Model Examination, February 2022

PG Department of Computer Applications & Artificial Intelligence, Semester 3

 Advanced Statistical Methods

Total : 80 marks                                                                    Time: 3 hours

Section A

Answer any 6 questions. Each question carries 3 marks.

(Write in not less than a paragraph)

1 .The random experiment has two outcomes,which can be called success and failure,probability for success in a single trial remains constant from trial to trial  of the experiment,The experiment is repeated finite number of times,Trials are independent.

2. 2To count the number of telephone calls arriving at a telephone switch board in unit time,to count the number of customers arriving at the super market per hour, to count the number of defective items etc

3. number of trials (n) is very large, p and q are almost equal,

4.refer text.

5. Binomial distribution summarises the number

6.to test the significance of difference between two variances,to test the equality of variances

7.standard deviation of sampling distribution of sample statistic.(write the equations also)

8. 1)  Level of Significance- probability of type 1 error2) type 1erreor-rejecting null hypothesis when it is true and type 2 errors- accepting null hypothesis when it is false

9.V(T1)<V(T2),explain

10. (p+-tv.SE)

11. frequency table which contains exactly 2 rows and columns.

12. small sample- when n is less than 30 and Large sample- when n is greater than 30

 

                                                                                                            (6 x 3 = 18 Marks)

Section B

Answer any 4 questions. Each question carries 8 marks.

(Write in not less than 2 pages)

 

13. n=6, use binomial formula,p=1/4(equating both sides)

14.  use poisson distribution formula,n=100,p=0.03,m=3,p(x)=0.0498* 243/120= 0.1008

15. apply normal  distribution formula,sd=12,population mean= 54,when x=46,z=-0.67,when x=56,z=0.17

Draw normal curve,p(-0.67<z<0.17)=0.2486+0.0675=0.3161,proportion=31.61%

16. Obtain the sampling distribution of the mean of samples from a population?

17.refer notefor additive property of chi-square distribution

18. when x follows a normal distributionz follows normal distribution.when z1,z2,……. Zk follows k normal variables then its sum follows chi-square distribution.if z is a normal and y is a chisquare variable  then z/sqrt(y/k) follows t distribution.if y1 and y2  are 2  chisquare variables with n1 and n2 df then y1/n1/y2/n2 follows F diastribution.

19. n=20,p=4/20,95% confidence interval=0.2+-1.96*0.089=(0.2-0.174, 0.2+0.174)

20. n= 26 , sample mean= 1200 , sample  SD of 150 ,  population mean =1300

Write the 5 steps use t test,se=30,t=-3.3, df=25 table value=2.06 at 0.05 level,rejected

21. 1+-1.96* sqrt(0.1*0.9/100= 4.12%,15.88%

 

            (4 x 8 = 32 Marks)

Section C

Answer up to 3 questions carrying 15 marks each. However, total marks for this section should not exceed 30 marks. Marks scored over 30 will be ignored

 

22. refer note

23. p(x<30)=0.17,when z=0.95,table value=0.33,-0.95= 30-mean/sd,given p(x>60)=0.17,p(z>b)=0.17, p(0<z<b)=0.33,mean=45,sd=15.8

24. refer note

25. write the test procedure,create table  with df=3,cv is greater than table value,reject null hypothesis.                                                                                                                         (Maximum 30 Marks)

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