Business Statistics And Research Methods — Part 1 MCQs with Explanations

The law of statistical regularity states that a moderately large number of items chosen at random from a large group will likely possess the same characteristics as the large group. This law is fundamental in sampling theory and ensures that a sample is representative of the population from which it is drawn. It relies on the principle of probability, which guarantees that random selection leads to an accurate reflection of the population's properties. This law is crucial in fields like business statistics where sampling is essential for data analysis.

Understanding Scales of Measurement: In statistics, we use different scales to measure data. Think of it like measuring things with different rulers. Nominal Scale: This is like labeling things with names. We just give them categories without any order or ranking. Example: Colors (red, blue, green), Gender (male, female), Types of cars (sedan, SUV, truck). Ordinal Scale: This scale has order or ranking, but the difference between each rank isn't necessarily equal. Example: Education level (high school, bachelor's, master's), Customer satisfaction (very satisfied, satisfied, neutral, dissatisfied, very dissatisfied). Interval Scale: Here, the difference between each point is equal, but there's no true zero point. Example: Temperature in Celsius or Fahrenheit (0°C doesn't mean there's no temperature). Ratio Scale: This scale has equal intervals and a true zero point. Zero means the absence of the thing being measured. Example: Height, weight, age, income. Applying it to the Question: The question asks about classifying respondents by gender (male, female). We're just assigning labels, not ranking or measuring anything numerically. Therefore, this is a nominal scale . Therefore, the correct answer is B: Nominal scale

Option A: Both correlation and regression coefficients have the same sign is generally true. Both correlation and regression coefficients can be positive or negative, indicating the direction of the relationship between variables. Option B: Arithmetic mean of the regression coefficients is always more than the correlation coefficient is false. The arithmetic mean of regression coefficients is not necessarily greater than the correlation coefficient. Option C: Regression coefficients are independent of both the origin and scale is generally true. Regression coefficients are not affected by changes in the origin or scale of the variables. Option D: Correlation coefficient is the square root of two regression coefficients is generally true. The correlation coefficient is the square root of the product of the two regression coefficients. Therefore, the correct answer is Option B: Arithmetic mean of the regression coefficients is always more than the correlation coefficient .

In sampling methods, both random and non-random techniques are employed to gather data from a population. Stratified Sampling: Explanation: This is a random sampling technique where the population is divided into subgroups or strata based on certain characteristics, and then samples are randomly selected from each stratum. Example: If a population is categorized by age, samples are randomly taken from each age group. Quota Sampling: Explanation: In quota sampling, the population is divided into specific groups, and a certain number of individuals are chosen from each group, not necessarily through a random process. Example: If a population is divided by gender, a quota of participants from each gender may be selected purposefully. Systematic Sampling: Explanation: In systematic sampling, a fixed interval is used to select samples after an initial random start. It is a structured approach but not entirely random. Example: Choosing every 5th person from a list after a random starting point. Cluster Sampling: Explanation: The population is divided into clusters, and then some clusters are randomly selected, and all members from those clusters are included in the sample. Example: If a city is divided into districts, randomly select some districts, and survey all individuals within those districts. In the context of the question, Quota Sampling is the non-random method as it involves selecting individuals purposefully based on certain quotas rather than entirely at random. Therefore, the correct answer is Option B: Quota sampling.

Stratified Sampling: Explanation: Stratified sampling is a restricted random sampling technique where the population is divided into subgroups or strata based on certain characteristics, and then samples are randomly selected from each stratum. Simple Random Sampling: Explanation: Simple random sampling is a pure random sampling technique where every individual in the population has an equal chance of being selected. Systematic Sampling: Explanation: Systematic sampling is a restricted random sampling technique where a random start point is chosen, and then every kth individual is selected. Multi-stage Sampling: Explanation: Multi-stage sampling involves a combination of various sampling techniques in multiple stages to create a more complex sampling design. In the context of the question, Simple Random Sampling is not a restricted technique; it is the most basic and unrestricted form of random sampling where each individual has an equal chance of being selected. Therefore, the correct answer is Option B: Simple random sampling .

Sampling error is the correct answer to “The difference between sample statistic and its corresponding population parameter is”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Both (A) and (R) are true is the correct answer to “Assertion (A): If regression coefficient of X on Y is greater than one, regression coefficient of Y on X must be less than one. Reason (R): The geometric mean between two regression coefficients is the coefficient of correlation.”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

0.4 is the correct answer to “If in Binomial distribution mean is 10 and standard deviation 2, q will be”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

3 alone is the correct answer to “Consider the following statements: 1. Quartile deviations is more instructive range as it discards the dispersion of extreme items 2. Coefficient of quartile deviaton cannot be used to compare the degree of variations in different distributions 3. There are 10 deciles for a series Which one of the above statements is/are correct”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Both (A) and (R) are correct, but (R) is not the correct explanation of (A) is the correct answer to “Assertion (A): A reasonably sized sample drawn randomly from large sized population contains almost all the characteristics which exist in the population. Reason (R): The theory of sampling is based on the two important laws of statistics, viz law of statistical regularity and law of inertia of large numbers.”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Rs. 26,422 is the correct answer to “The regression equation of profits (X) on sales (Y) of a firm is given as: 3Y - 5X + 10 = 0. If the sales of the firm is Rs. 44,000, the profit will be”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Ordinal data is the correct answer to “Assignment of numerals to the objects to represent their attributes is known as”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Ogive is the correct answer to “A graph of a cumulative frequency distribution is called”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

a-3, b-4, c-1, d-2 is the correct answer to “Match the following in the term of Terms and Explanation : List-I (Terms) List-II (Explanation) a. $$\frac{{{Z^2} \cdot \sigma _p^2}}{{{e^2}}}$$ 1. Measurement for Kurtosis b. $$\frac{{\left| {\overline {{X_1}} - \overline {{X_2}} } \right|}}{{\sqrt {\sigma _p^2\left( {\frac{1}{{{n_1}}} + \frac{1}{{{n_2}}}} \right)} }}$$ 2. Calculated value of $$F$$ ratio c. $$\frac{{{\mu _4}}}{{\mu _2^2}}$$ 3. Statistical approach to find out the size of sample d. $$\frac{{\sigma _{{s_1}}^2}}{{\sigma _{{s_2}}^2}}$$ 4. Calculated $$z$$ value of mean differences”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Regression is the correct answer to “The under root of two . . . . . . . . coefficients gives us the value of correlation coefficients.”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

'F' test is the correct answer to “Among the following choose the most suitable 'test' that can be applied to examine the influence of one factor on different groups.”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Statements I and II is the correct answer to “Consider the following statement and identify the wrong statements. Statement I: Accepting null hypothesis, when it is false, is called a level of significance. Statement II: $$1 - \alpha $$ is called power of a test. Statement III: Critical value of $$Z$$ - static for two-tailed test at 5% level of significance is 1.96.”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

P(B) × P(A/B) is the correct answer to “In case of conditional probability (A and B) =”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Interview is the correct answer to “In a predominantly illiterate area consisting of 10,000 population, data has to be collected from 10% of them. The appropriate technique for data collection would be”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

$$\frac{{\left( {1 - {r^2}} \right)}}{{\sqrt n }}$$ is the correct answer to “Which one of the following formulas is used to calculate the standard error of coefficient of correlation between 25 paired observations of a sample”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Coefficient of variation is an absolute measure of dispersion is the correct answer to “Which one of the following is a false description”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Market power is the correct answer to “The Learner Index measures”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

The square root of the product of their regression coefficients is the correct answer to “Karl Pearson's coefficient of correlation between two variables is”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Rank correlation coefficient is the correct answer to “When quantitative measures for certain factors cannot be fixed the measure which is generally adopted is known as”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Statement I is true, while Statement II is false is the correct answer to “Statement I: If the alternative hypothesis is as $$\mu \ne {\mu _0}$$ ; a researcher requires two-tailed test in hypothesis-testing. Statement II: The mean of the sampling distribution of mean is not equal to the parametric value of mean.”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

0.80 is the correct answer to “If unexplained variation between variables X and Y is 36%, what is the coefficient of correlation between the variables”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Inductive Reasoning is the correct answer to “A reasoning where we start with certain particular statements and conclude with a universal statement is called:”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Sequencing of data is the correct answer to “Process of arranging data into a new order is called”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

To test the hypothesis about a single population variance is the correct answer to “From the following, identify one situation where 'F' test cannot be used.”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Ratio-to-moving average method is the correct answer to “The most widely used method of measuring seasonal variations is”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Number of classes in a continuous distribution is the correct answer to “Sturge's rule is used to find out directly”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

A research initiated to solve an immediate problem is the correct answer to “Action research that is usually meant for professional people is:”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

In percentage is the correct answer to “The index number express-”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

A graph of a cumulative frequency distribution is the correct answer to “An ogive is:”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

The time it takes a randomly selected student to complete an exam is the correct answer to “Which one of these variables is a continuous random variable”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Investigation is the correct answer to “Normally the reports present conclusions are based on:”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

a-3, b-4, c-1, d-2 is the correct answer to “Match the items of List I with the items of List-II and select the correct answer: List-I List-II a. Contingency coefficient for any size of contingency table 1. $$\sqrt {\frac{{N - n}}{{N - 1}}} $$ b. Statistical approach to decide size of a sample 2. $$\frac{{{\sigma _p}}}{{\sqrt n }}$$ c. Finite population multiplier 3. $$\sqrt {\frac{{{x^2}}}{{{x^2} + n}}} $$ d. Standard error of mean 4.$$\frac{{{Z^2} \cdot \sigma _p^2}}{{{e^2}}}$$”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Y-intercept is the correct answer to “In the regression equation Y = a + b X, a is called:”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Line graph is the correct answer to “To show the trend for a variable, which one of the presentation method is used”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.

Coefficient of variation is the correct answer to “Which one of the following is a relative measures of dispersion”. This question is standard in competitive examination syllabi for Business Statistics And Research Methods.