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L15.2082 - Statistics for Business and Economics (2024/2025)

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In a box there are two green balls and two red balls. Consider that two balls are randomly selected without replacement. The probability of these two balls having the same color is:

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Consider the histogram depicted below:

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Which boxplot depicts the same data as the histogram?

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Consider the research question: “How frequently do adults consume fruits and vegetables?”

A survey asks a random sample of participants to report their daily intake of fruits and vegetables, but some respondents overstate their consumption to appear healthier.

Which type of bias is most likely present?
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Consider the following statements referring to the use of the addition rule and to the use of the multiplication rule in probability theory:

  • We multiply when we see [K] for independent events;
  • We add when we see [Y] for mutually exclusive events;
  • We can still multiply for dependent events when we see [W] but we do so using [Z] probability;

What stands for K, Y , W and Z, respectively?

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In a specific region, the probability of a thunderstorm occurring during the summer season is 0.3. The probability of heavy rainfall during the summer season is 0.4. The probability of both a thunderstorm and heavy rainfall occurring during the summer season is 0.2. What is the probability that there will be either a thunderstorm or heavy rainfall (or both) during the summer season?

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Two events are said to be independent if the occurrence of one event:

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A sports league has two skill assessment tests: a fitness test and a technical skills test. Suppose 20% of athletes fail the fitness test, 15% fail the technical skills test, and 5% fail both.

If an athlete is randomly chosen, what is the probability that this athlete fails at least one of the tests?
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Researchers study the effect of urban green spaces on air quality by comparing pollution levels in different European cities, some with extensive green parks and others with little green space.

What is the unit of analysis in this study?
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A company wanted to assess the effectiveness of its leadership training program. Managers who voluntarily completed the training were compared to those who did not. Surveys showed that trained managers reported greater confidence. The survey was conducted with all managers across the company.

We can conclude that:
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Consider the frequency table below displaying the number of parking tickets that a random sample of 140 individuals got in the last month. 

          

          
085
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218

Knowing that the sample mean is 0.521, what is the mean absolute deviation? Present you result with two decimal values. 

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