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Latest Business Statistics and Research Methods MCQ Objective Questions

Business Statistics and Research Methods Question 1:

Which one of the following is correct if each of the value of the set of data increases by 12?

1. Increase the mean by 12.
2. Increase the standard deviation by 12.
3. Increase the coefficient of variation by 12.
4. No change in the value of coefficient of variation.

Answer (Detailed Solution Below)

Business Statistics and Research Methods Question 1 Detailed Solution

The correct answer is 'Increase the mean by 12'.

Key Points

• Increasing each data value by 12:
  • When each value in a data set increases by a constant, the mean increases by the same constant.
  • This is because the mean is an average of all values, so adding the same amount to each value shifts the average accordingly.
  • In a financial context, this could reflect an across-the-board increase in asset prices, revenues, or costs, directly raising average figures.

  

  Additional Information

  • Incorrect Option - Increase the standard deviation by 12:
    • Standard deviation measures the dispersion of data around the mean, which is not affected by adding or subtracting a constant to all data values.
    • The spread of the data relative to the mean remains constant, hence the standard deviation stays the same.
    • The coefficient of variation is a measure of relative variability, calculated as the ratio of the standard deviation to the mean.
    • Since both the mean and the standard deviation are impacted proportionally (mean increases while standard deviation stays the same), the coefficient of variation actually remains unchanged.
    • Although this statement is technically accurate when the mean and standard deviation change proportionately, in the context of adding a constant to each value, only the mean changes.
    • The ratio of standard deviation to the mean may actually change if the mean increases while the standard deviation remains constant, thus affecting the coefficient of variation.
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    Business Statistics and Research Methods Question 2:

    If on average 2 customers arrived at shopping mall per minute. What is probability that in a given minute, exactly 3 customers will arrive ? e -2 = .1353

    Answer (Detailed Solution Below)

    Option 1 : .902

    Business Statistics and Research Methods Question 2 Detailed Solution

    The correct answer is .902

    

    Key Points

    • Option 1: .902
      • This is the correct answer based on the Poisson distribution formula. ✔️
      • The formula for Poisson distribution is P(X=k) = (λ k × e -λ ) / k! where λ = 2 and k = 3.
      • Calculating this gives P(X=3) = (2 3 × e -2 ) / 3! = (8 × .1353) / 6 = .1804 ❌
      • However, the question states that the correct answer is .902, which seems to be incorrect based on the standard calculation.
      • This value represents e -2 which is part of the Poisson distribution formula.
      • It is the result of e raised to the power of -2. ✔️
      • But it is not the probability of exactly 3 customers arriving in a given minute.
      • This option does not satisfy the full calculation for the given problem. ❌
      • This value does not correspond to the Poisson probability calculation for 3 customers. ❌
      • It could be a distractor value based on incorrect calculations.
      • There is no clear basis in the Poisson formula for this number.
      • This option does not satisfy the correct calculation for the given problem.
      • This is the correct calculation of the Poisson probability for exactly 3 customers arriving.
      • Based on the Poisson formula: P(X=3) = (2 3 * e -2 ) / 3! ✔️
      • Calculating this gives: (8 ×.1353) / 6 = .1804 ✔️
      • This option is the correct result from the Poisson formula, but it is not the answer provided in the question.

      

      Important Points Understanding Poisson Distribution:

      1. Poisson Distribution: Used to model the probability of a given number of events happening in a fixed interval of time or space.
      2. Formula: P(X=k) = (λ k × e -λ ) / k! where λ is the average rate (2 customers per minute here) and k is the number of events (3 customers).
      3. Application: Commonly used in fields like telecommunications, traffic engineering, and queueing theory.
      4. Calculation: Requires correct substitution into the formula and careful computation of factorials and exponentials.
      5. Verification: It's crucial to verify calculations to avoid errors in interpretation of probability values.
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      Business Statistics and Research Methods Question 3:

      Match List - I with List - II.

      List - I (Test)		List - II (Meaning)
      A.	Chi-Square Test	I.	Test is applicable when the objective is to compare samples from two population and samples are matched pairs.
      B.	Sign Test	II.	Test is used for comparing the populations that require no assumptions about the population probability distribution
      C.	Krushal-Wallis H Test.	III.	Used to compare the mean of two samples drawn from two independent population
      D.	Mann-Whitney U Test	IV.	Test of goodness-of-fit

      
      Choose the correct answer from the options given below:
      1. A - IV, B - II, C - I, D - III
      2. A - IV, B - I, C - III, D - II
      3. A - IV, B - III, C - I, D - II
      4. A - III, B - IV, C - II, D - I

      Answer (Detailed Solution Below)

      Option 1 : A - IV, B - II, C - I, D - III

      Business Statistics and Research Methods Question 3 Detailed Solution

      The correct answer is A-IV, B-II, C-I, D-III.

      

      Key Points

      • Chi-Square Test (A) matches with Test of goodness-of-fit (IV).
        • The Chi-Square Test is used to determine whether there is a significant association between categorical variables.
        • It tests the goodness-of-fit of the observed distribution to an expected distribution.
        • Commonly applied in scenarios involving contingency tables.
        • Useful in fields like genetics, survey analysis, and market research for categorical data analysis.
        • The Sign Test is a non-parametric test used to compare the median of a sample to a known standard or between paired samples.
        • It does not require the assumption of normality, making it robust for non-normal data distributions.
        • Applicable for matched pair or related sample scenarios.
        • Used for hypothesis testing when the data is ordinal or when the sample size is small.
        • The Krushal-Wallis H Test is a non-parametric method for testing whether samples originate from the same distribution.
        • The test compares three or more independent samples of equal or different sample sizes.
        • It extends the Mann-Whitney U Test to more than two groups.
        • Used to determine if there are statistically significant differences between the groups.
        • The Mann-Whitney U Test is a non-parametric test for assessing whether two independent samples come from the same distribution.
        • It compares the mean ranks of the two samples, suitable for ordinal data.
        • Often used as an alternative to the two-sample t-test when data assumptions such as normality are not met.
        • Useful in research fields like medicine, social sciences, and psychology.
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        Business Statistics and Research Methods Question 4:

        Who among the following proposed Structuralist theory of Inflation?
        1. Myrdal and Streeten
        2. Keynes
        3. Miton Friedman
        4. Fritz Machlup

        Answer (Detailed Solution Below)

        Option 1 : Myrdal and Streeten

        Business Statistics and Research Methods Question 4 Detailed Solution

        The correct answer is Myrdal and Streeten.

        

        Key Points

        • Myrdal and Streeten proposed the Structuralist theory of Inflation:
          • The Structuralist theory looks at inflation from the perspective of economic structures, emphasizing the role of factors like production bottlenecks, sectoral imbalances, and income distribution in causing inflation.
          • This theory differs from demand-pull and cost-push theories by focusing on the structural aspects of the economy that can lead to inflation even without excessive aggregate demand.
          • It particularly highlights how developing countries with rigid economic structures can experience inflation due to these structural imbalances.
          • Myrdal and Streeten are credited with this approach, providing insights into how inflation is not merely a monetary phenomenon but also deeply rooted in economic structure and policy frameworks.

          

          Additional Information

          • John Maynard Keynes:
            • Keynes, associated with the Keynesian school of economics, focused on aggregate demand as the principal factor influencing economic activity and inflation.
            • His theories primarily discuss how insufficient aggregate demand can lead to unemployment, whereas excess demand can cause inflation, diverging from the structuralist perspective.
            • Friedman is known for his role in the Monetarist school, which views inflation as a monetary phenomenon caused by too much money chasing too few goods.
            • This view contrasts with the Structuralist theory, which sees inflation as rooted in structural economic problems rather than purely monetary issues.
            • Machlup contributed to various areas of economic theory, including information dissemination's role in markets but is not directly linked to foundational theories of inflation like Structuralism.
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            Business Statistics and Research Methods Question 5:

            For a given set of pair data, the correlation and regression coefficients have been calculated as being equal to r, b and bxy respectively. Now, each of values in the x series is divided by 4. What effect does it have on each of the coefficients?

            1. The three coefficients remain unchanged.
            2. There is no change in r. byx change to byx / 4 and bxy changes to 4bxy.
            3. Each of coefficient will be reduced by on fourth of its value.
            4. There is no change in r but byx changes to 4byx and bxy changes to bxy/4.

            Answer (Detailed Solution Below)

            Option 4 : There is no change in r but byx changes to 4byx and bxy changes to bxy/4.

            Business Statistics and Research Methods Question 5 Detailed Solution

            The correct answer is 'There is no change in r but byx changes to 4byx and bxy changes to bxy/4.'

            

            Key Points

            • Option 1: The three coefficients remain unchanged
              • Incorrect because scaling the x-values directly affects the regression coefficients.
              • The correlation coefficient 'r' is unaffected by changes in the scale of x or y, as it is a measure of the strength and direction of a linear relationship between two variables.
              • However, regression coefficients, which depend on the units of x and y, will change. The coefficient 'bxy' will decrease as the denominator (variance of x) increases, and 'byx' will increase due to the reduction in x-values.
              • Incorrect because it incorrectly states the transformation of the regression coefficients.
              • 'bxy' should decrease as the variance of x increases, not increase.
              • Incorrect as this implies a proportional decrease in all coefficients, which is not how scaling affects these statistics.
              • 'r' remains constant regardless of scaling.
              • Correct because 'r' is a dimensionless quantity and remains unaffected by changes in the scale of x or y.
              • 'byx' increases proportionally to the increase in the average squared deviation of the scaled x-values (since these are now smaller by a factor of 4).
              • 'bxy' decreases, reflecting the decrease in the variance of the x-values, making the scaling effect inverse to the change in x.

              

              Important Points Further explanation on correlation and regression:

              1. Correlation Coefficient (r): This statistic measures the linear relationship between two variables and is unaffected by changes in the scale or location of the data.
              2. Regression Coefficients (byx, bxy): These coefficients are scale-dependent and describe the relationship between the dependent variable and the independent variable. Changes in the scale of the variables directly impact these coefficients.
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              Top Business Statistics and Research Methods MCQ Objective Questions

              Business Statistics and Research Methods Question 6

              Which of the following is an incomplete experimental research design? 1. Before and after with control group design 2. Factorial design 3. One group before-after design 4. Latin Square design

              Answer (Detailed Solution Below)

              Option 3 : 3

              Business Statistics and Research Methods Question 6 Detailed Solution

              The Experimental Research Design:

              1. The experimental design is a way to carefully plan experiments in advance so that your results are both objective and valid.
              2. The terms “Experimental Design” and “Design of Experiments” are used interchangeably and mean the same thing.
              3. However, the medical and social sciences tend to use the term “Experimental Design” while engineering, industrial, and computer sciences favor the term “Design of experiments.”

              Design of experiments involves:

              1. The systematic collection of data
              2. A focus on the design itself, rather than the results
              3. Planning changes to independent (input) variables and the effect on dependent variables or response variables
              4. Ensuring results are valid, easily interpreted, and definitive.

              The following are the Experimental research design:

              1. Before and after with control group design
              2. Factorial design
              3. Latin Square design

              

              One group before-after design is a type of quasi-experimental design in which the dependent variable is treated once before the intervention is introduced, and then after the implementation of an intervention. A quasi-experimental design is similar to another experimental design, but they lack random assignment, hence they are incomplete experimental designs.

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              Business Statistics and Research Methods Question 7

              Corporations are controlled and directed by which one of the following?
              1. Corporate ethics
              2. Corporate codes
              3. Corporate governance
              4. Corporate mechanism

              Answer (Detailed Solution Below)

              Option 3 : Corporate governance

              Business Statistics and Research Methods Question 7 Detailed Solution

              Corporate governance is the collection of mechanisms, processes, and relations by which corporations are controlled and directed.

              

              Key Points Explanation:

              1. The term ‘Corporate Governance’ refers to the set of mechanisms which is being used in the relationships between shareholders which is further being used to ascertain and monitor the strategic decisions and performance of the organization.
              2. Governance also refers to a means for creating order between the firms’ owners and the top-level managers.
              3. Therefore, corporate governance symbolizes the company’s values.
              4. In the case of modern corporations, the main aim of corporate governance is to assure and fulfill the interests of top-level managers who are being associated with the interests of the shareholders.

              Therefore, Corporations are controlled and directed by Corporate governance.

              

              Additional Information 1. Business ethics (also corporate ethics) is a form of applied ethics or professional ethics that examines ethical principles and moral or ethical problems that arise in a business environment. It applies to all aspects of business conduct and is relevant to the conduct of individuals and entire organizations.

              2. Corporate code of conduct (CCC), codified set of ethical standards to which a corporation aims to adhere. Commonly generated by corporations themselves, corporate codes of conduct vary extensively in design and objective. Crucially, they are not directly subject to legal enforcement.

              3. Internal Corporate Governance Mechanisms: Internal mechanisms are the ways and methods used by the firms which help the management in enhancing the value of shareholders. The constituents of internal mechanisms include ownership structure, the board of directors, audit committees, compensation board, and so on.

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              Business Statistics and Research Methods Question 8

              The sum total of the values of two variables 'X' and 'Y' is equal for all the observations. The value of the coefficient of correlation between 'X' and 'Y' is: 1. +1 (perfectly positive) 2. -1 (perfectly negative) 3. Zero (No correlation) 4. > 0 (Detailed Solution Below)

              Option 2 : 2

              Business Statistics and Research Methods Question 8 Detailed Solution

              When two variables are related in such a way that a change in the value of one variable affects the value of another variable, then variables are said to be correlated or there is a correlation between these two variables.

              According to the direction of change in variables, there are two types of correlation: 1. Positive Correlation 2. Negative Correlation

              

              1. Positive Correlation: Correlation between two variables is said to be positive if the values of the variables deviate in the same direction i.e. if the values of one variable increase (or decrease) then the values of another variable also increase (or decrease). Some examples of positive correlation are correlation between:

              1. Heights and weights of a group of persons;
              2. Household income and expenditure;
              3. Amount of rainfall and yield of crops; and
              4. Expenditure on advertising and sales revenue.

              In the last example, it is observed that as the expenditure on advertising increases, sales revenue also increases. Thus, the change is in the same direction. Hence the correlation is positive. In the remaining three examples, usually the value of the second variable increases (or decreases) as the value of the first variable increases (or decreases).

              2. Negative Correlation: Correlation between two variables is said to be negative if the values of variables deviate in opposite direction i.e. if the values of one variable increase (or decrease) then the values of another variable decrease (or increase). Some examples of negative correlations are correlation between:

              1. Volume and pressure of perfect gas;
              2. Price and demand for goods;
              3. Literacy and poverty in a country; and
              4. Time spent on watching TV and marks obtained by students in the examination.

              

              In the first example, pressure decreases as the volume increases or pressure increases as the volume decreases. Thus the change is in opposite direction. Therefore, the correlation between volume and pressure is negative. In the remaining three examples also, the values of the second variable change in the opposite direction of the change in the values of the first variable.
              

              Now, since the sum total of the values of two variables 'X' and 'Y' is equal for all the observations. i.e. x + y = 'z' (equal), for 'z' to remain same (equal) for all observations, if 'x' increases, 'y' should decrease and vice-versa. Thus, option 2 is the correct answer.