BSc Business Administration Mock Exam - Business Mathematics PDF

Name, First Name ________________________________ (in capital letters) Matriculation-No. __________________ Class: _________ Mock Exam...

Name, First Name ________________________________ (in capital letters) Matriculation-No. __________________ Class: _________ Mock Exam ☒ AS ☐ SS BSc Business Administration (IM) Module: Business Mathematics and Statistics 1 Part Statistics Lecturer: Prof. Dr. Tobias Schoch Date: ………. Campus: ☒ Olten ☐ Basel ☐ Brugg-Windisch Time: 120 minutes Allowed material: ☐ Calculator TI-30 ☐ Calculator TI-84 ☐ Laptop ☐ No materials allowed ☐ Other:................................................................................................ Note:  Please put your name down on all the sheets at the beginning of the examination.  Write down your answers only on the sheets provided.  If there is not enough space, continue your answers on the back of the sheet. If there still is not enough space, ask for further sheets.  Do not use any sheets of your own.  Do not write in pencil. (Exception: graphs) Points: Maximum points achieved (without Learning Points) Lecturer/ Points PAC* Points Exam Learning Total Examination Part Points Total Points Module Grade: ☐ 1.0 ☐ 1.5 ☐ 2.0 ☐ 2.5 ☐ 3.0 ☐ 3.5 ☐ 4.0 ☐ 4.5 ☐ 5.0 ☐ 5.5 ☐ 6.0 *PAC: Performance Assessment in Class 1  Name, First Name ________________________________ Problem 1 (10 points) Short questions. a) Consider the two events 𝐴 = {1, 2, 3} und 𝐵 = {2, 4, 6} of throwing an ideal dice with sample space Ω = {1, 2, 3, 4, 5, 6}. We denote the complement of an event by superscript “C”. Are the following mathematical statements true or false? Tick the correct box. 𝐴 ∪ 𝐵 = Ω. ☐ true ☐ false 𝐴 ∩ 𝐵 = {2}. ☐ true ☐ false 𝐴𝐶 ∩ 𝐵 = {4, 6}. ☐ true ☐ false b) The calculated correlations of the four scatter plots (see below) are -0.85, -0.09, 0.58, and 0.99. Which one is which? A: B: C: D: A B C D c) Statements: True or false? Tick the correct box. A large correlation (in absolute value) is a sign of a causal ☐ true ☐ false relationship. Standard deviation and interquartile range are both measures ☐ true ☐ false of dispersion. A large positive correlation between the variables 𝑥𝑖 and 𝑦𝑖 ☐ true ☐ false implies that the slope b of the linear regression 𝑦𝑖 = 𝑎 + 𝑏 ⋅ 𝑥𝑖 + 𝑒𝑖 (where 𝑒𝑖 denotes the error) is also large. 2  Name, First Name ________________________________ Problem 2. (12 points) In a (clinical) memory experiment, the investigator communicates 30 words to a group of persons and ask them to memorize the words. After a short break, each test persons had to write down all the words she/he could recall. For a sample of 𝑛 = 10 persons, the number of recalled words 𝑥𝑖 are tabulated in the following table. 𝑖 1 2 3 4 5 6 7 8 9 10 𝑥𝑖 7 19 16 14 15 9 12 16 11 24 Answer the following questions. a) Is the statistical distribution of the recalled words 𝑥𝑖 symmetric? Substantiate your answer with a calculation that tells whether the data are symmetric or not. b) Suppose that tabulated 𝑥-data are visualized in a boxplot. Is observation 𝑥10 marked as an outlier in the boxplot? Substantiate your answer with a calculation. c) The 𝑥-data are grouped/ binned into the following brackets [5,10), [10,15), [15,20), and [20,25). Compute the relative frequencies of the brackets. Note: Round the results to two decimal digits. 3  Name, First Name ________________________________ Problem 3. (12 points) A consulting company examined the key figures of 120 restaurants. The analysis focused on the relationship between the restaurants' profits (in US$) and their number of customers. The following graph shows the scatterplot for the two variables and the regression line (see also the regression table below). Note: The variables are given in per 1’000 units. Table: Regression of profit on the number of customers (restaurant) Coefficient Std. Error t-Value P-Value (Constant) -56.29 ** 21.00 -2.68 0.01 Number of customers 8.30 *** 1.39 5.99