Samacheer Kalvi Class 12 Business Maths Solutions Chapter 8 Sampling Techniques and Statistical Inference Exercise 8.3

Choose The Correct Answer:

Question 1. A ................ may be finite or infinite according as the number of observation or items in it is finite or infinite
(a) population
(b) census
(c) parameter
(d) none of the options
Answer: (a) population
In simple words: A population in statistics can be counted or uncounted based on how many things are in it. It is the whole group that you are interested in.

🎯 Exam Tip: Remember that the 'population' refers to the entire group or set of items being studied, whether it's small and countable or very large and uncountable.

Question 2. A ................ of statistical individuals in a population is called a sample.
(a) Infinite set
(b) finite subset
(c) finite set
(d) entire set
Answer: (b) finite subset
In simple words: A sample is a smaller, countable part taken from a larger group (the population). It helps us understand the whole group without checking every single item.

🎯 Exam Tip: A sample is always a part of the population and is typically finite, even if the population itself is infinite, to make analysis practical.

Question 3. A finite subset of statistical individuals in a population is called ....................
(a) a sample
(b) a population
(c) universe
(d) census
Answer: (a) a sample
In simple words: When you pick a small, countable group of items from a larger group of statistical individuals, that small group is called a sample. This small group helps represent the larger one.

🎯 Exam Tip: This question reinforces the definition of a sample as a finite part of a population. Always remember these fundamental definitions.

Question 4. Any statistical measure computed from sample data is known as ....................
(a) Parameter
(b) Infinite measure
(c) uncountable

🎯 Exam Tip: Statistical measures from sample data are called statistics, while measures from population data are called parameters. Knowing the difference is key in statistical inference.

Question 5. A ................ is one where each item in the universe has an equal chance of known opportunity of being selected
(a) Parameter
(b) random sample
(c) statistic
(d) entire data
Answer: (b) random sample
In simple words: A random sample is when every single item in a large group has the same fair chance of being picked. This helps make the sample truly represent the whole group.

🎯 Exam Tip: Random sampling is fundamental for ensuring that a sample is representative and that the results can be generalized to the entire population.

Question 6. A random sample is a sample selected in such a way that every item in the population has an equal chance of being included
(a) Harper
(b) fisher
(c) karl pearson
(d) Dr. yates
Answer: (a) Harper
In simple words: This definition of a random sample, where every item has an equal chance of being picked, was given by Harper. It highlights the fairness of the selection process.

🎯 Exam Tip: When definitions are attributed to specific individuals, it's important to remember them as they often appear in multiple-choice questions.

Question 7. Which one of the following is probability sampling
(a) Purposive sampling
(b) sample random sampling
Answer: (b) sample random sampling
In simple words: Probability sampling methods ensure that every part of the population has a known chance of being chosen. Simple random sampling is a good example of this, as it gives everyone an equal chance.

🎯 Exam Tip: Understand the difference between probability sampling (where selection is random and known) and non-probability sampling (where selection is based on convenience or judgment).

Question 8. In simple random sampling of drawing any unit, the probability of drawing any unit at the draw is ?
(a) \( \frac { n }{N} \)
(b) \( \frac { 1 }{N} \)
(c) \( \frac { N }{n} \)
(d) n
Answer: (b) \( \frac { 1 }{N} \)
In simple words: In simple random sampling, if there are N total units, the chance of picking any one specific unit is just one out of N. Each unit has the same chance.

🎯 Exam Tip: For simple random sampling, the probability of selecting any single unit is always 1 divided by the total population size (N).

Question 9. In ................ the heterogeneous groups divided into homogeneous groups
(a) Non-probability sample
(b) a sample random sample
(c) a stratified random sample
(d) Systematic sample
Answer: (c) a stratified random sample
In simple words: Stratified random sampling means you first sort a mixed group into smaller, similar groups. Then, you pick samples from each of these smaller groups separately.

🎯 Exam Tip: Stratified sampling is especially useful when the population is diverse, as it ensures representation from all important subgroups.

Question 10. Errors in sampling are of
(a) Two types
(b) three types
(c) four types
(d) five types
Answer: (a) Two types
In simple words: When we take a sample, there are mainly two kinds of errors that can happen: sampling error and non-sampling error. These errors can affect how accurate our results are.

🎯 Exam Tip: The two main types of errors in sampling are sampling error (due to observing a sample instead of the whole population) and non-sampling error (due to mistakes in data collection, processing, etc.).

Question 11. The method of obtaining the most likely value of the population parameter using statistic is called
(a) estimate
(b) estimate
(c) biased estimate
(d) standard error
Answer: (d) standard error
In simple words: The standard error tells us how much the sample mean might differ from the actual population mean. It's a measure of how good our sample is at predicting the whole population.

🎯 Exam Tip: Standard error quantifies the precision of a sample statistic, showing how much sample estimates vary from sample to sample.

Question 12. An estimator is a sample statistic used to estimate a
(a) population parameter
(b) biased estimate
(c) sample size
(d) census
Answer: (a) population parameter
In simple words: An estimator is a calculation based on sample data that we use to guess the value of something about the whole population. For example, using the average of a sample to guess the average of the population.

🎯 Exam Tip: Remember that a 'statistic' describes a sample, and we use a 'statistic' as an 'estimator' to infer something about a 'parameter' of the population.

Question 13. ................ is a relative property, which states that one estimate is efficient relative to another.
(a) efficiency
(b) sufficiency
(c) unbiased
(d) consistency.
Answer: (a) efficiency
In simple words: Efficiency in statistics means that one way of estimating something is better than another if it gives a more accurate guess using the same amount of data. It compares how well different estimates work.

🎯 Exam Tip: An efficient estimator is one that has the smallest variance among all unbiased estimators, meaning it's generally more precise.

Question 14. If probability \( p[|\bar { 0 } – 0|< < \epsilon|] 1 \to \mu \) as \( n \to a \) for any positive then \( \bar { \theta} \) is said to estimator of \( \theta \)
(a) efficient
(b) sufficient
(c) unbiased
(d) consistent
Answer: (d) consistent
In simple words: An estimator is called "consistent" if, as you use more and more data (make your sample size bigger), your estimate gets closer and closer to the true value. It always improves with more information.

🎯 Exam Tip: Consistency ensures that an estimator will eventually get very close to the true parameter value as the sample size increases indefinitely.

Question 15. An estimator is said to be ................ if it contains all the information in the data about the parameter it estimates.
(a) efficient
(b) sufficient
(c) unbiased
(d) consistent
Answer: (b) sufficient
In simple words: A sufficient estimator uses all the useful information from the sample data to estimate the population value. It means no other estimator could give you more insight from the same data.

🎯 Exam Tip: Sufficiency is a key property, meaning that a sufficient statistic captures all the information about a parameter that is available in the sample.

Question 16. An estimate of a population parameter given by two numbers between which the parameter would be expected to lie called an ................ interval estimate of the parameter
(a) point estimate
(b) interval estimate
(c) standard error
Answer: (b) interval estimate
In simple words: An interval estimate gives you a range of numbers, not just one, where the actual population value is likely to be found. It gives a sense of certainty about where the true value lies.

🎯 Exam Tip: Differentiate between a point estimate (a single value) and an interval estimate (a range of values), both used for population parameters.

Question 17. A ................ is a statement or an assertion about the population parameter
(a) hypothesis
(b) statistic
(c) sample
(d) census
Answer: (a) hypothesis
In simple words: A hypothesis is an idea or a guess you make about a population value. You then test this idea using data to see if it is likely to be true or false.

🎯 Exam Tip: A hypothesis is the starting point for statistical testing, a testable claim or statement about a population parameter.

Question 18. Type I error is
(a) Accept \( H_0 \) when it is true
(b) Accept \( H_0 \) when it is false
(c) Reject \( H_0 \) when it is true
(d) Reject \( H_0 \) when it is false
Answer: (c) Reject \( H_0 \) when it is true
In simple words: A Type I error happens when you decide that a null hypothesis is wrong, but it was actually right. It's like a "false alarm."

🎯 Exam Tip: Remember Type I error as 'rejecting a true null hypothesis' – analogous to a false positive in a test.

Question 19. Type II error is?
(a) Accept \( H_0 \) when it is wrong
(b) Accept \( H_0 \) when it is when it is true
(c) Reject \( H_0 \) when it is true
(d) Reject \( H_0 \) when it is false
Answer: (a) Accept \( H_0 \) when it is wrong
In simple words: A Type II error happens when you decide that a null hypothesis is right, but it was actually wrong. It's like missing something important that was really there.

🎯 Exam Tip: Remember Type II error as 'failing to reject a false null hypothesis' – analogous to a false negative in a test.

Question 20. The standard error of sample mean is?
(a) \( \frac { \sigma }{\sqrt{2n}} \)
(b) \( \frac { \sigma }{n} \)
(c) \( \frac { \sigma }{\sqrt{n}} \)
(d) \( \frac { \sigma^2}{\sqrt{n}} \)
Answer: (c) \( \frac { \sigma }{\sqrt{n}} \)
In simple words: The standard error of the sample mean tells us how much the average of our sample is likely to vary from the real average of the entire population. We find it by dividing the population standard deviation by the square root of the sample size.

🎯 Exam Tip: This formula is crucial for understanding how sampling variability affects the precision of the sample mean as an estimator of the population mean.