Tribhuvan University MBS First Semester Statistical Methods Exam Question 2082 (2025)

Tribhuvan University, Faculty of Management, Office of the Dean · Statistical Methods (MBS First Semester) · 2082 BS · Semester Examination — 11 questions — a free old question paper on Goodone.club’s exam-paper archive.

  1. (a) A student wishes to examine the impact of the size and age of a firm on its performance in a particular industry. Size is measured by the number of employees, age by the number of years the firm has operated, and performance by return on equity. For firms A–F, respectively: performance (Rs lakhs) = 10, 3, 27, 12, 6, 3; size = 20, 2, 19, 33, 29, 8; age = 25, 30, 25, 7, 15, 18. (i) Find the multiple-regression equation for predicting performance from size and age. (ii) Estimate performance when firm size is 10 and age is 20. (iii) Compute the standard error of estimate and interpret the resu... [30 marks]
  2. (a) A car manufacturer receives 40% of its tyres from supplier I, 30% from supplier II, and 30% from supplier III. Past records show defect rates of 2%, 3%, and 1%, respectively. If a randomly selected tyre is defective, find the probability that it was supplied by (i) supplier I, (ii) supplier II, and (iii) supplier III. (b) The gender and position of managers are: male—junior 50, middle 60, senior 100 (total 210); female—junior 60, middle 50, senior 40 (total 150). Column totals are 110, 110, and 140; grand total 360. Test whether manager position and gender are associated, using the chi-squ... [15 marks]
  3. (a) A random variable X follows the binomial distribution with n = 10 and p = 0.25. Find (i) P(X < 5), (ii) P(X ≤ 5), and (iii) P(X ≥ 7). (b) To study the effectiveness of physical exercise for weight reduction, eight people followed a prescribed program for one month. Their weights before exercise were 209, 178, 169, 212, 180, 192, 158, and 180 pounds; their corresponding weights after exercise were 196, 171, 170, 207, 177, 190, 159, and 180 pounds. At the 1% level of significance, test whether the prescribed exercise program is effective. [15 marks]
  4. (a) Two laboratories independently produce drugs intended to relieve arthritis. The first drug was tested on 200 patients and 120 obtained relief. The second was tested on 150 patients and 80 obtained relief. Test at the 5% level of significance whether the effectiveness of the two drugs differs significantly. (b) The observed mistakes per page in a book were: mistakes per page 0, 1, 2, 3, 4; corresponding numbers of pages 211, 90, 19, 5, 0; total 325. Fit a Poisson distribution to the data. [15 marks]
  5. (a) The average length of stay for a certain type of patient in a chronic-disease hospital is 60 days with standard deviation 15 days. Assuming an approximately normal distribution, find the probability that a randomly selected patient has a stay (i) longer than 50 days, (ii) shorter than 30 days, and (iii) between 30 and 80 days. (b) Two independent manufacturing processes produce the same item. A sample of 250 items from one process has mean weight 120 grams and standard deviation 10 grams; a sample of 400 items from the other process has mean weight 124 grams and standard deviation 12 grams... [15 marks]
  6. The simple correlation coefficients between temperature (X₁), rice yield (X₂), and rainfall (X₃) are r₁₂ = 0.59, r₁₃ = 0.46, and r₂₃ = 0.70. Calculate (i) the partial correlation coefficient r₁₂.₃ and (ii) the multiple correlation coefficient R₁.₂₃. [5 marks]
  7. A coin is tossed 400 times and heads appear 240 times. Can the coin be regarded as unbiased? Use the 5% level of significance. [5 marks]
  8. A tyre-company quality-control manager has a sample of 100 tyres with a mean life of 30,214 km. The population standard deviation is known to be 860 km. Construct 95% and 99% confidence limits for the mean life of that brand of tyre. [5 marks]
  9. The numbers of students and variances of marks in a test are: boys—number 11, variance 81; girls—number 10, variance 121. Using an F-test at the 5% level of significance, test whether the variability of the boys' and girls' marks is the same. [5 marks]
  10. From a group of 8 children containing 5 boys and 3 girls, 3 children are selected at random. Calculate the probabilities that the selected group contains (i) no girl and (ii) 2 boys and 1 girl. [5 marks]
  11. Write short notes on: (a) systematic random sampling; (b) simple random sampling. [5 marks]