Statistics I

Daffodil International University Faculty of Science & Information Technology Department of Information Technology & Management Mid-Term Examination, Spring 2024 Course Code: STA 101; Course Title: Statistics I Sections & Teachers: All Time: 2.0 Hrs Marks: 40 Answer ALL Questions [The figures in the right margin indicate the full marks and corresponding course outcomes. All portions of each question must be answered sequentially.] 1. a) Explain the difference between marginal probability, joint probability, and conditional probability using a real-life example, such as student performance and attendance. [Marks-3] CO-1 Level-2 b) Compare the mean, median, and mode of the following data [Marks-2] 10, 18, 12, 11, 12, 14, 13. 2. a) Discuss simple and multiple regression with example. Also write the model of the simple and multiple regression. [Marks-4] CO-2 Level-2 b) Illustrate how measures of dispersion—such as range, variance, and standard deviation—help in understanding the spread of the following data set: 10, 18, 12, 11, 12, 14, 13 [Marks-4] 3. A fitness coach gathered data on the number of weekly workout sessions and the weight loss in kg after one month for 7 clients: CO-3 Level-3 SL | 1 | 2 | 3 | 4 | 5 | 6 | 7 Workout Sessions | 1 | 2 | 2 | 3 | 4 | 5 | 5 Weight Loss (kg) | 0.5 | 1 | 1.3 | 1.8 | 1.7 | 2 | 2.2 (a) Classify dependent and independent variable of the data with explanation. [Marks- 3] (b) Demonstrate scatter diagram with explanation [Marks- 2] (c) Calculate the correlation coefficient between workout sessions and weight loss. [Marks- 3] (d) Determine the regression equation and interpret the coefficient [Marks- 4] (e) Predict and interpret the expected weight loss for a client who works out 6 times a week using the regression model [Mark - 2] (f) Compute residual for the client who works out 4 times a week. [Mark - 2] (g) Demonstrate the regression equation. [Mark - 2] 4. In a survey of 135 people, 78 like Coffee, 55 like Tea, and 30 do not like both Coffee and Tea. (a) Draw a venn diagram to present the data [Mark - 2] CO-4 Level-3 (b) Find the probability that a person selected at random likes only Coffee. [Mark - 2] (c) What is the probability that a person selected at random likes either Coffee or Tea, but not both? [Mark - 2] (d) What is the probability that a person selected at random likes Coffee, given that the person does not like Tea. [Mark - 2] Formula Mean(μ) = ∑_{i=1}^n x_i / n σ^2 = 1/N ∑_{i=1}^N (x_i - μ)^2 s^2 = 1/(n - 1) ∑_{i=1}^n (x_i - x̄)^2 r = (∑xy - (∑x)(∑y)/n) / sqrt([∑x^2 - (∑x)^2/n][∑y^2 - (∑y)^2/n]) α = ȳ - βx̄ β_yx = (∑(xy) - (∑x)(∑y)/n) / (∑x^2 - (∑x)^2/n) P(A) = Favourable case / Total case P(A|B) = P(A ∩ B) / P(B)