# Statistics-I – BSc.CSIT (TU) Question Paper 2068 | First Semester

## First Semester | First Year | Tribhuvan University Computer Science and Information Technology (Stat. 108) Subject: Statistics-I , Year: 2068 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. Write the importance of sampling over census. Describe systematic sampling. In a population with N = 6 the values of Y are 8, 3, 1, 11, 4 and 7. Calculate the sample Mean $\bar{y}$for all possible simple random samples without replacement of size 2. Verify that $\bar{y}$ is an unbiased estimate of $\bar{Y}$.
2. The following data represent the operating times in hours for three types of scientific pocket calculators before a recharge is required:
 Calculator A 4.9 6.1 4.3 4.6 5.3 5.5 Calculator B 5.4 6.2 5.8 5.5 5.2 4.8 Calculator C 6.4 6.8 5.6 6.5 6.3 6.6

Use the Kruskal-Wallis test, at the 0.01 level of significance, to test the hypothesis that the operating times for all three calculators are equal.

3. The following table shows the scores(Y) made by ten assembly line employees on a test designed to measure job satisfaction. It also shows the scores made on an aptitude test (X1) and the number of days absent (X2) during the past year (excluding vacations).
 Y X1 X2 70 6 1 60 6 2 80 8 1 50 5 8 55 6 9 85 9 0 75 8 1 70 6 1 72 7 1 64 6 2

The summation values are as following:
ΣY = 681, ΣX1 = 67, ΣX2 = 26, ΣX1Y = 467, ΣX2Y = 1510
ΣX1X2 = 153, ΣY2 = 47455, ΣX12 = 463, ΣX22 = 158
(i) Calculate the least squares equation that best describes these three variables.
(ii) Predict the value of scores when aptitude test is 7 and number of days absent is 6.

Group B

Answer any eight questions:   (8 x 5 = 40)

4. Show that in simple random sampling without replacement sample mean is unbiased estimate of population mean.
5. What do you mean by partial correlation coefficient? State the relationship between simple and partial correlation coefficient when there are three variables. If r12= 0.5, r23 = 0.1 and r13 = 0.4, compute r12.3 and r23.1
6. Explain two stage sampling with sample mean and corresponding variance.
7. Differentiate parametric and non parametric test.
8. In an industrial production line, items are inspected periodically for defectives. The following is a sequence (from left to right) of defective items, D, and non defective items, N, Produced by this production line:
 D D N N N D N N D D N N N N N D D D N N D N N N N D N D

Use run test with a significance level 0.05 to determine whether the defectives are occurring at random or not.

9. Use the sign test to see whether there is a difference between the numbers of days required days required to collect an account receivable before and after a new collection policy. Use the 0.05 significance level.
 Before 33 36 41 32 39 47 34 29 32 After 35 29 38 34 37 47 36 32 30
10. A random sample of 200 married men, all retired, was classified according to education and number of children.
 Education Number of Children 0-1 2-3 Over 3 Elementary 14 37 32 Secondary 19 42 17 College 12 17 10

Test the hypothesis, at the 0.05 level of significance, that the number of children is independent of the level of education attained by the father.

11. Write Cobb-Douglas production function with interpretation of the regression coefficients.
12. Suppose the residuals for a set of data collected over 8 consecutive time periods are as follows:
 Time Period 1 2 3 4 5 6 7 8 Residuals -4 -3 -3 -2 1 1 3 7

Compute the first order autocorrelation.

13. Explain the term multicollinearity and describe a situation where the problem of multicollinearity arises?
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