## First 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

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 + 18X_{1} + 20 X_{2}

Sample size (n) = 28

Total sum of squares (TSS) = 250

Sum of squares due to error (SSE) = 100

Standard error of regression coefficient of X_{1}(Sb_{1} ) = 3.2

Standard error of regression coefficient of X_{2}(Sb_{2} ) = 5.2

i) Predict the value of Y for X_{1} = 15 and X2= 25

ii) Test the significance of regression coefficient of X_{2}

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, is an unbiased estimator of .

5) What do you mean by partial correlation coefficient? State the relationship between simple and partial correlation coefficients when there are three variables. If r_{12} = 0.5, r_{23} = 0.1 and r_{13} = 0.4, compute r_{12.3} and r_{23.1}

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:

N N N N Y Y N Y Y N Y N N N N

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.