Podcast
Questions and Answers
What is the correlation coefficient that implies a strong positive relationship between two variables?
What is the correlation coefficient that implies a strong positive relationship between two variables?
Which statement is true regarding a large correlation?
Which statement is true regarding a large correlation?
How many words did the investigator communicate in the memory experiment?
How many words did the investigator communicate in the memory experiment?
Which measure indicates the spread of the number of recalled words in the memory experiment?
Which measure indicates the spread of the number of recalled words in the memory experiment?
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What is the name of the graphical representation that could show the outlier in the number of recalled words?
What is the name of the graphical representation that could show the outlier in the number of recalled words?
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If the recalled words are grouped into brackets, how many words fall into the bracket [15,20)?
If the recalled words are grouped into brackets, how many words fall into the bracket [15,20)?
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In the given data set, which of the options below reflects a non-symmetric distribution?
In the given data set, which of the options below reflects a non-symmetric distribution?
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Based on the number of recalled words, which statement is true about the standard deviation?
Based on the number of recalled words, which statement is true about the standard deviation?
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What does the symbol $A^C$ represent in the context of set theory?
What does the symbol $A^C$ represent in the context of set theory?
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Which of the following correctly describes the event $A imes B$?
Which of the following correctly describes the event $A imes B$?
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What is the result of the operation $A imes B$ where $A = \{1, 2, 3}$ and $B = \{2, 4, 6}$?
What is the result of the operation $A imes B$ where $A = \{1, 2, 3}$ and $B = \{2, 4, 6}$?
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How many elements are present in the union of sets A and B ($A igcup B$)?
How many elements are present in the union of sets A and B ($A igcup B$)?
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Which statement correctly describes the intersection $A igcap B$?
Which statement correctly describes the intersection $A igcap B$?
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What is the complement of set B, denoted $B^C$, in this scenario?
What is the complement of set B, denoted $B^C$, in this scenario?
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If $A = \{1, 2, 3}$ and $B = \{2, 4, 6}$, is the statement $A igcap B = {2}$ true or false?
If $A = \{1, 2, 3}$ and $B = \{2, 4, 6}$, is the statement $A igcap B = {2}$ true or false?
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Which of the following correctly states the relationship between the events A and B?
Which of the following correctly states the relationship between the events A and B?
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Flashcards
𝐴 ∪ 𝐵 = Ω
𝐴 ∪ 𝐵 = Ω
The union of two sets contains all elements present in either set. '𝐴 ∪ 𝐵' is true because all elements from 1 to 6 are present in either '𝐴' or '𝐵'.
𝐴 ∩ 𝐵 = {2}
𝐴 ∩ 𝐵 = {2}
The intersection of two sets contains only elements that are common to both sets. '𝐴 ∩ 𝐵' is true because '2' is the shared element between '𝐴' and '𝐵'.
𝐴𝐶 ∩ 𝐵 = {4, 6}
𝐴𝐶 ∩ 𝐵 = {4, 6}
The complement of a set includes all elements that are not in the original set. '𝐴𝐶' includes elements not in '𝐴', and '𝐵' contains '4' and '6' not found in '𝐴𝐶', making the statement true.
Correlation Coefficient
Correlation Coefficient
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Positive Correlation
Positive Correlation
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Negative Correlation
Negative Correlation
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Range of Correlation Coefficient
Range of Correlation Coefficient
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Scatterplot
Scatterplot
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Standard Deviation vs. Interquartile range
Standard Deviation vs. Interquartile range
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Correlation and Causation
Correlation and Causation
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Slope of Linear Regression
Slope of Linear Regression
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Study Notes
Mock Exam - Business Mathematics and Statistics 1
- Module: Business Mathematics and Statistics 1
- Lecturer: Prof. Dr. Tobias Schoch
- Date: Brugg-Windisch
- Campus: Olten/Basel
- Time: 120 minutes
- Allowed Material: Calculator TI-30, Laptop, Other (Specify)
- Notes: Put name on all sheets, answer on provided sheets, write on back, use additional sheets if needed. No pencil unless graphs, no own sheets.
Part Statistics - Mock Exam
- Maximum Points: (Details on how many marks per problem)
- General Notes:
- The mock exam gives an impression of the final exam
- Only covers part of relevant topics (refer to module description)
- Largely based on previously discussed exercises in class
- Does not serve as further exercises; further problems are in the compulsory reading.
Problem 1 - Short Questions (10 points)
- Part a): True or false questions regarding sets and events (A, B)
- A ∪ B = Ω (True/False)
- A ∩ B = {2} (True/False)
- AC ∩ B = {4, 6} (True/False)
- Part b): Matching scatter plots to correlations:
- Four scatter plots with given correlations (-0.85, -0.09, 0.58, 0.99) related to A, B, C, D
- Correlation to Scatter plots
- Part c): True or false questions on correlation and dispersion
- A large correlation signifies a causal relationship (True/False)
- Standard deviation and interquartile range are both measures of dispersion (True/False)
- A large positive correlation between variables x and y implies a large slope in a linear regression (True/False)
Problem 2 - (12 points)
- Memory Experiment Data:
- 10 participants recalled a set of 30 words
- Number of words recalled (xi) for each participant in given table.
- Part a): Assess symmetry of recalled words' distribution
- Part b): Identify if x10 is an outlier in a boxplot
- Part c): Calculate relative frequencies for grouped x-data in brackets (5,10), (10,15), (15,20), (20,25).
Problem 3 - (12 points)
-
Restaurant Profit and Customers: Examines a regression model of restaurants' profits vs. customer count
- Scatterplot of profit against the number of customers (in 1000s)
- Regression table with data like Constants, Coefficients, Standard error (Std. Error), t-value, P-Value
-
Part a): Write regression model formula
-
Part b): Describe relationship between profit and customers (in terms of tendency).
- Describe the relationship/tendency between variable A and variable B based on the regression results (e.g. positive association).
-
Part c): Profit prediction for a restaurant with 22,000 customers.
Problem 4 - (8 points)
- Father-Son Professions: Analyzing data about professions of fathers and sons.
- Contingency Table (provided). Missing entries and marginal totals.
- Part a): Add missing data to the table
- Part b): Probability of son being a day laborer given the father is a workman.
- Part c): Probability that a son is a day laborer given his father is a workman.
Problem 5 - (12 points)
- Counting Problems: Counting possibilities for words and teams/arrangements.
- Part a): Number of two-letter words (XYZ alphabet).
- Part b): Number of possible football teams from 20 players (given a fixed goal keeper).
- Part c): Number of ways to arrange 5 people in a queue.
- Part d): Probability of winning lottery jackpot (choosing 6 out of 45 numbers).
Problem 6 - (8 points)
- Customer Payment Times: Analyzing payment data of 500 customers
- Part a): Probability that a customer pays by invoice.
- Part b): Probability that a customer pays by invoice and in time.
- Part c): Probability that a customer pays in time if they pay online.
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Description
Prepare for your final exam with this mock exam covering key concepts from Business Mathematics and Statistics 1. This exam will simulate the conditions of the final, with a focus on statistics-related problems, including set theory and probability. Make sure to utilize your calculator TI-30 and familiarize yourself with the exam format.
