Quantitative Methods Quiz No 2

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[ Quantitative Method Quiz No 2 ]

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Quantitative Methods: An In-Depth Overview

Quantitative methods are vital tools for scientific investigation and practical applications in various fields. They rely on structured data and statistical techniques to derive objective conclusions. This article will explore the main elements of quantitative methods, emphasizing their principles, applications, and the distinctions between various research approaches.


Understanding Quantitative Methods

Quantitative methods are research techniques that gather and interpret numerical data. Unlike qualitative methods, which focus on subjective experiences, quantitative methods are objective, providing results that can be replicated and generalized. This approach is especially valuable in fields like economics, psychology, social sciences, and business.


Core Principles of Quantitative Research

Quantitative research follows specific principles to ensure that data collection and analysis yield valid, reliable results. These principles include the focus on measurable outcomes, the use of controlled variables, and structured data collection. Such consistency allows researchers to build upon previous findings and advance knowledge.


Primary Elements of Quantitative Research


Measurement

Measurement is the process of assigning numerical values to variables to make them comparable. Whether assessing income levels, response times, or population sizes, accurate measurement is crucial for reliability. Measurement scales vary, from nominal scales (categorizing data) to interval and ratio scales that provide precise values.


Reliability and Validity

Reliability ensures that a study's findings are consistent over time, while validity ensures that the research accurately measures what it intends to. Together, reliability and validity strengthen a study’s credibility and support its findings' applicability in real-world settings.


Data Analysis

Data analysis in quantitative research involves processing raw data to uncover patterns, relationships, and trends. Analysis methods range from simple calculations, like averages, to complex multivariate models. Software tools such as SPSS, R, and Python have streamlined data analysis, making it accessible to a broader range of researchers.


Types of Quantitative Research Design

Quantitative research design varies depending on the study's purpose, objectives, and the nature of the variables.


Cross-Sectional Studies

Cross-sectional studies analyze data from a population at one specific point in time. This design is ideal for identifying correlations and understanding population characteristics but cannot determine cause-and-effect relationships.


Longitudinal Studies

Longitudinal studies track the same variables over an extended period, revealing changes and trends. This approach is valuable in medical research, where long-term data is essential for understanding disease progression or treatment efficacy.


Experimental Studies

Experimental studies manipulate independent variables to observe their effects on dependent variables. By using controlled settings, researchers can draw strong cause-and-effect conclusions, making this design ideal for psychological, educational, and scientific research.


Survey-Based Studies

Survey-based studies rely on questionnaires and structured interviews to gather quantitative data from large samples. This approach is often used in social sciences and marketing research to gain insights into preferences, behaviors, and attitudes.


Key Statistical Techniques in Quantitative Analysis


Correlation and Causation Analysis

Correlation analysis examines the strength and direction of relationships between variables. While correlation does not imply causation, it provides useful information that can guide further investigation.


Multivariate Analysis

Multivariate analysis explores multiple variables simultaneously to understand complex relationships. Techniques like multiple regression and structural equation modeling help identify how multiple factors influence an outcome, offering a detailed view of variable interactions.


Predictive Modeling

Predictive modeling uses historical data to forecast future outcomes. Regression analysis, time-series analysis, and machine learning algorithms are commonly used in fields like finance, marketing, and supply chain management to make informed predictions.


Hypothesis Testing and Significance

Hypothesis testing determines if a result is statistically significant or due to chance. Techniques such as the t-test, chi-square test, and ANOVA allow researchers to evaluate their hypotheses objectively, establishing confidence in their findings.


Applications of Quantitative Methods Across Fields


Economics and Finance

In economics, quantitative methods assess trends, forecast market movements, and analyze economic policies. Financial analysts use these methods for investment analysis, portfolio management, and risk assessment, relying on data to support decisions.


Social Sciences

Quantitative methods in social sciences investigate social phenomena like income disparity, voting behavior, and public health trends. Survey data, census records, and large datasets enable sociologists and policymakers to assess social patterns and inform policy changes.


Engineering and Technology

Engineers use quantitative methods to analyze system performance, conduct quality control, and optimize processes. Data analysis aids in identifying production bottlenecks, improving efficiency, and innovating new solutions in manufacturing, IT, and product development.


Healthcare and Medicine

In healthcare, quantitative methods support clinical trials, patient outcome studies, and epidemiological research. Hospitals and healthcare providers rely on statistical analysis to improve treatment effectiveness, measure patient satisfaction, and monitor public health trends.


Advantages and Challenges of Quantitative Research


Advantages

  • Precision and Objectivity: Quantitative methods produce objective data that is easy to interpret and replicable.
  • Broader Generalization: Large sample sizes allow findings to be generalized across populations.
  • Data-Driven Insights: Statistics and models provide precise answers, making quantitative research ideal for forecasting.

Challenges

  • Limited Contextual Depth: Quantitative methods may overlook the nuances that qualitative data captures.
  • Resource Demands: Data collection and analysis require substantial resources, including time, money, and specialized skills.
  • Difficulty in Complex Measurement: Some concepts, like human behavior or emotions, are challenging to measure quantitatively, which can reduce result accuracy.

Quantitative Research and Ethics

Ethics play a significant role in quantitative research, especially when human participants are involved. Researchers must obtain informed consent, ensure data privacy, and avoid deceptive practices. Ethical standards guide research design and execution, ensuring that findings are both valid and respectful of participants' rights.


Conclusion

Quantitative methods are instrumental in advancing knowledge across numerous disciplines. By focusing on structured data and statistical analysis, they offer reliable, precise insights that can guide policies, inform business strategies, and support scientific discoveries. Although these methods have limitations, their strengths make them a foundational tool for evidence-based research. Mastering quantitative techniques allows researchers to produce impactful, data-driven findings that contribute to progress in diverse fields.

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1. From a given finite population, samples are drawn with replacement. If the sample size is decreased from 70
to 45. The standard error would:

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2. Tom and Jerry both invested same amount for 8 years. If Tom’s rate of return is 9% and Jerry’s rate is 10%
compounded annually then how much more percent amount Jerry will have after 8 years than Tom?

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3. Which of the following statements is/are correct about random sample?
(i) It is bias free sample
(ii) Where every member of the population has an equal chance of being selected as a member of the sample

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4. There are 5 red and 7 black cars for sale at fast wheels. If 2 cars are sold, what is the probability that both are
black?

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5. Which of the following statements as regards to variance is/are correct?
(i) It is always smaller than the standard deviation
(ii) It can never be negative.

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6. There is a two-digit number and 4 times the sum of its digits and 12 times the difference of its digits makes
the number. If the number is x y. Which of the following will give the number after simultaneous solution?

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7. Simplify: x + 10 = 11x^2 + 1

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8. If Ahmad saves 1000 in the first month and 500 more every month, how much time he needs to save
Rs.45000?

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9. Hashim invested Rs. 20000 today and will withdraw amount after two years. What will be the amount if he
withdraws after 3 years at 12% compounded annually?

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10. Geometric Mean of 7, 14 and  21?

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11. Which of the following statements about scatter diagram is/are correct?

  • (i) It leads to more accurate results if the collected data is a typical
    (ii) we can draw it for two or more variables

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12. An investment of 1.5 million is made in a business for 4 years and gain is 0.5 million. Find rate of gain under
compound interest?

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13. If the discount rate is 12%, The present value of Rs. X received at the end of each year for the next five years
is equal to:

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14. A wallet contains 65 notes of Rs.1000 and 35 notes of Rs.500. Four notes are selected at random. Find the
probability that sum of notes are Rs.3000?

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15. If Present value is 1000000 and interest is 750000 in 4years and 10 months. Find the simple interest rate?

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16. Which of the following statements about scatter diagram is/are correct?
(1) It is important to establish which variable is independent before plotting
(ii) It might indicate a relationship where there is none

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17. Which of the following statements about Laspayer’s Price Index is/are correct?
(i) It tends to overstate inflation.
(ii) The denominator does not change from year to year.

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18.

Consider the following information:
Claim: Population proportion =p<0.7
Proportion standard deviation = 0.0092
Sample proportion = 0.684
Level of significance = 10%
n is more than 30
Test is on tail
Test the hypothesis whether to accept or reject the null hypothesis:

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19. A company invested 9 million. Interest rate was 8%, 12% and 14% per year for first, second and third year
respectively. Find NPV if cost of capital is 9%

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20. Which of the following statements about scatter diagram is/are correct?
(i) Shows visual relation between variables.
(ii) It might indicate a relationship, where there is none.

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21. Eight runners have equal chance of winning the race. What is the probability that a person wins the bet if he
selects top 3 runners in the correct order?

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22. A 4-digit pin code can begin with any number except 0 & 1. If repetition of the same digit is allowed, the
probability of a pin code begins with 5 and end with a 2 is?

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23. If two dices are rolled then probability of appearing exactly two six?

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24. There are 85% chances of winning a match of team. Find the probability that it wins exactly 4 matches out of 5?

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25. True about mean:
(i) Most repeated value
(ii) The best single figure to describe data

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