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Business Mathematics and Statistics · Class 12 Commerce

Ch 8Sampling Techniques and Statistical Inference — Class 12 Business Mathematics and Statistics, concept-first.

In business and economic analysis we rarely have direct access to every unit of a population — the complete set of items, people, or transactions under study (e.g., every customer of a bank, every unit produced in a year).

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Key concepts

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Methods of Sampling

A sample is a subset of the population selected for study in place of a full census. The commonly used probability sampling methods are:

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Chapter contents

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Population, Sample, Census and Sample Survey

In business and economic analysis we rarely have direct access to every unit of a population — the complete set of items, people, or transactions under study (e.g., every customer of a bank, every uni…

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Methods of Sampling

A sample is only useful for inference if it is drawn in a way that gives it a fair chance of representing the population — this is why how a sample is selected matters as much as how many units are in…

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Sampling Error and Non-Sampling Error

Whenever conclusions about a population are drawn from a sample rather than a census, some amount of error is unavoidable. Statisticians distinguish two broad kinds:

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Standard Error of the Sample Mean

The standard error (SE) of a sample statistic measures how much that statistic would be expected to vary from one random sample to another of the same size — in effect, it is the yardstick that turns…

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Estimation: Point and Interval Estimates

Estimation is the process of using a sample statistic to infer the value of an unknown population parameter. There are two kinds of estimates:

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Hypothesis Testing: Framework and Errors

Hypothesis testing is the statistical procedure used to decide, on the basis of sample evidence, whether a claim (or assumption) about a population is likely to be true.

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Large-Sample Z-Test for a Single Mean

When the sample size is large (, by the usual convention) and either the population standard deviation is known or the sample standard deviation is used as a close approximation to it, a claim about t…

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Chi-Square Test for Independence of Attributes

The chi-square () test of independence examines whether two categorical (qualitative) attributes observed on the same set of units are statistically independent of each other, or whether they are asso…

Exercises

+Show 8 questions8 questions
  1. Q6Distinguish between a census and a sample survey. Give one business situation where a census would be necessary and one where a sample surve…Free
  2. Q7Distinguish between Stratified Sampling and Cluster Sampling. Why might a researcher prefer stratified sampling over cluster sampling when t…Free
  3. Q8Explain the difference between sampling error and non-sampling error. State whether each of the following is an example of sampling error or…Free
  4. Q9The population standard deviation of the monthly sales (in Rs. '000) of a chain's outlets is known to be Rs. 15,000 (i.e., sigma = 15 in Rs.…Preview
  5. Q10A random sample of 225 customer bills has a mean value of Rs. 200 with a population standard deviation of Rs. 30. Construct a 99% confidence…Preview
  6. Q11A pharmaceutical quality-control team tests each batch of tablets with H0: 'the batch meets the required purity standard.' Explain what a Ty…Preview
  7. Q12State, with a reason, whether each of the following calls for a one-tailed or a two-tailed test: (a) a tyre company wants to test whether a…Preview
  8. Q13A firm installs a new machine claiming it raises the average hourly output of a process to at least 250 units, up from the earlier average.…Preview

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 26 questions26 questions
  1. Q1For testing $H_0 : \mu = \mu_0$ against $H_1 : \mu < \mu_0$, what is the critical value at $\alpha = 0.01$ ? (a) $-1.645$ (b) $-2.33$ (c) $2…Preview
  2. Q2In simple random sampling from a population of $N$ units, the probability of drawing any unit at the first draw is : (a) $\dfrac{N}{n}$ (b)…Preview
  3. Q3Type II error is : (a) Accept $H_0$ when it is false (b) Reject $H_0$ when it is false (c) Reject $H_0$ when it is true (d) Accept $H_0$ whe…Preview
  4. Q4Mention two branches of Statistical Inference.Preview
  5. Q5A die is thrown $9000$ times and a throw of $3$ or $4$ is observed $3240$ times. Find the standard error of the proportion for an unbiased d…Preview
  6. Q6A ______ of statistical individuals in a population is called a sample. (a) finite set (b) infinite set (c) entire set (d) finite subsetPreview
  7. Q7A ______ is one where each item in the universe has an equal chance of known opportunity of being selected. (a) statistic (b) parameter (c)…Preview
  8. Q8The standard error of sample mean is : (a) $\frac{\sigma}{\sqrt{n}}$ (b) $\frac{\sigma}{\sqrt{2n}}$ (c) $\frac{\sigma^2}{\sqrt{n}}$ (d) $\fr…Preview
  9. Q9The standard deviation of a sample of size 50 is 6.3. Determine the standard error whose population standard deviation is 6.Preview
  10. Q10A finite subset of statistical individuals in a population is called ________. (a) universe (b) a sample (c) census (d) a populationPreview
  11. Q11An estimator is sample statistics used to estimate a : (a) sample size (b) population parameter (c) census (d) biased estimatePreview
  12. Q12State any two merits of simple random sampling.Preview
  13. Q13Find the sample size for the given standard deviation 10 and the standard error with respect of sample mean is 3.Preview
  14. Q14"A random sample is a sample selected in such a way that every item in the population has an equal chance of being included" is said by : (a…Preview
  15. Q15An estimator is said to be __________ if it contains all the information in the data about the parameter it estimates. (a) unbiased (b) effi…Preview
  16. Q16The standard deviation of a sample of size 50 is 6.3. Determine the standard error whose population standard deviation is 6 ?Preview
  17. Q17A sample of 100 measurements at breaking strength of cotton thread gave a mean $7.4$ g and a standard deviation of $1.2$ g. Find 95% confide…Preview
  18. Q18A __________ is one where each item in the universe has an equal chance of known opportunity of being selected. (a) statistic (b) parameter…Preview
  19. Q19Errors in sampling are of : (a) four types (b) two types (c) five types (d) three typesPreview
  20. Q20In a sample of 400 population from a village, 230 are found to be eaters of vegetarian items and the rest non-vegetarian items. Compute the…Preview
  21. Q21A die is thrown 9000 times and a throw of 3 or 4 is observed 3240 times. Find the standard error of the proportion for an unbiased die.Preview
  22. Q22Any statistical measure computed from sample data is known as ________. (a) Finite measure (b) Parameter (c) Uncountable measure (d) Statist…Preview
  23. Q23The standard error of sample mean is : (a) $\frac{\sigma}{\sqrt{n}}$ (b) $\frac{\sigma}{\sqrt{2n}}$ (c) $\frac{\sigma^2}{\sqrt{n}}$ (d) $\fr…Preview
  24. Q24What is Type I error ?Preview
  25. Q25A wholesaler in apples claims that only 4% of the apples supplied by him are defective. A random sample of 600 apples contained 36 defective…Preview
  26. Q26(a) The mean breaking strength of cables supplied by a manufacturer is 1,800 with a Standard Deviation 100. By a new technique in the manufa…Preview

More questions

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  1. Example 1A retail chain has 800 employees, spread across 40 branches with 20 employees at each branch; the branches are further grouped into 4 region…Free
  2. Example 2A quality-control department finds that the population standard deviation of the fill-weight of a certain packaged product is 20 gm. If a ra…Free
  3. Example 3A sample of 100 invoices from a firm's ledger has a mean value of Rs. 150 (in hundreds) with a known population standard deviation of Rs. 25…Preview
  4. Example 4A packaging machine is set to fill packets with an average of 500 gm of a product, with a known population standard deviation of 40 gm. A ra…Preview
  5. Example 5A firm surveyed 100 employees to see whether attitude towards a proposed new HR policy (For / Against) is independent of gender. The results…Preview