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Statistics-I – BSc.CSIT (TU) Question Paper 2065 | First Semester

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stat I question paper 2065First Semester | First Year | Tribhuvan University
Computer Science and Information Technology (Stat. 108)
Subject: Statistics-I , Year: 2065
Old Question Collection | Question Bank

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Full Marks: 60 | Pass Marks: 24 | Time: 3 hours.

Candidates are required to give their answers in their own words as far as practicable.
All notations have the usual meanings.

Group A

Attempt any two:     (2×10=20)

1) Differentiate simple random sampling and stratified random sampling. Show that

i) In simple random sampling without replacement (SRSWOR), the sample mean is an unbiased estimate of the population mean.
ii) In SRSWOR, the variance of the sample mean is given by
Var \left( \bar{y_n} \right) = \dfrac{S^2}{n}. \dfrac{N-n}{N}

2) Test the hypothesis of no difference between the ages of male and female employees of a certain company using the Mann-Whitney U test for the sample data. Use the 0.10 level of Significance.

Males 31 25 38 33 42 40 44 26
Females 44 30 34 47 35 32 35 47

3) Suppose you are given following information with n = 28.
Multiple regression model ̇Y = 5 + 18X1 + 20 X2
Sample size (n) = 28
Total sum of squares (TSS) = 250
Sum of squares due to error (SSE) = 100
Standard error of regression coefficient of X1(Sb1 ) = 3.2
Standard error of regression coefficient of X2(Sb2 ) = 5.2

i) Predict the value of Y for X1 = 15 and X2= 25
ii) Test the significance of regression coefficient of X2
iii) Compute the coefficient of multiple coefficient of determination.

Group B

Answer any eight questions: (8×5=40)

4) Show that in two stage sampling with SRSWOR at both stages, \bar{y} is an unbiased estimator of \bar{Y}.

5) What do you mean by partial correlation coefficient? State the relationship between simple and partial correlation coefficients when there are three variables. If r12 = 0.5, r23 = 0.1 and r13 = 0.4, compute r12.3 and r23.1

6) Define cluster sampling with sample mean and variance of sample mean.

7) For what conditions non parametric test is used. Explain some important non parametric test.

8) The weights of 4 people before they stopped smoking, in kilogram are as follows:

Before 66 80 69 52 75
After 71 82 68 56 73

Use the signed-rank test for paired observations to test the hypothesis, at 0.05 level of significance, that giving up smoking has no effect on a person’s weight against the alternative that one’s weight increases if he or she quits smoking

9) A random sample of 15 adults living in a small town is selected to estimate the proportion of voting favoring a certain candidate for mayor. Each individual was also asked if he or she was a college graduate. By letting Y and N designate the responses of “yes” and “no” to the education question, the following sequence was obtained:
Use the runs test at the 0.1 level of significance to determine if the sequence supports the contention that the sample was selected at random.

10) In an experiment to the study the dependence of hypertension on smoking habits, the following data were taken on 180 individuals:

Non Smokers Moderate Smokers Heavy Smokers
Hypertension 21 36 30
No Hypertension 48 26 19

Test the hypothesis that the presence or absence of hypertension is independent of smoking habits. Use a 0.05 level of significance.

11) Define dummy variable. What condition should be necessary for fitting logistic regression?

12) Suppose the residuals for a set of data collected over 9 consecutive time periods are as follows:

Time period 1 2 3 4 5 6 7 8
Residuals -2 -3 =2 -1 0 1 4 -2

Compute the Durbin Watson statistics. At the 0.05 level of significance, is there evidence of auto correlation among the residuals?

13) Describe a multiple regression model with its assumption. Also describe the method of obtaining its parameters.

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