Chapter Exam

Chapter 8: Sampling Techniques and Statistical Inference — Online MCQ Test

Q: A statistical measure calculated from the population data is known as a ________.

Answer: B. Parameter — A parameter is a characteristic value of the population (such as population mean or variance), whereas a statistic is calculated from sample data.

Q: What is the formula for the Standard Error of the sample mean when sampling is done from an infinite population with population standard deviation σ?

Answer: C. σ / √n — The standard error of the sample mean (S.E.) for an infinite population or with-replacement sampling is given by σ / √n.

Q: For a sample of size n = 100 drawn from a normal population with standard deviation σ = 15, what is the standard error of the sample mean?

Answer: A. 1.5 — Standard Error (S.E.) = σ / √n = 15 / √100 = 15 / 10 = 1.5.

Q: When testing a hypothesis about a single population mean with a small sample (n < 30), which of the following conditions strictly requires using the Student's t-test instead of the standard normal Z-test?

Answer: C. The population is normal and population variance is unknown. — Student's t-test is applied when the sample size is small (n < 30), the parent population is normal, and the population variance (σ²) is unknown, forcing the use of sample variance (s²).

Q: A simple random sample of size n = 40 is drawn without replacement from a finite population of size N = 400. If the population variance is σ², which of the following expressions correctly represents the variance of the sample mean V(x-bar)?

Answer: C. (σ² / 40) * (360 / 399) — For Simple Random Sampling Without Replacement (SRSWOR), the variance of the sample mean is V(x-bar) = (σ²/n) * ((N - n) / (N - 1)). Substituting n = 40 and N = 400 yields (σ²/40) * (360 / 399).

BUSINESS MATHS AND STATISTICS · CLASS 12th · Tamil Nadu State Board

Practice Chapter 8: Sampling Techniques and Statistical Inference with a free chapter-wise online MCQ test for Tamil Nadu State Board CLASS 12th BUSINESS MATHS AND STATISTICS. This chapter covers: This chapter covers random sampling methods parameter estimation and statistical hypothesis testing. Students examine large and small sample tests z-tests t-tests chi-square tests.... AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 8: Sampling Techniques and Statistical Inference — Important Questions & Answers (FAQ)

Frequently asked questions from Tamil Nadu State Board CLASS 12th BUSINESS MATHS AND STATISTICS — Chapter 8: Sampling Techniques and Statistical Inference, with answers and explanations. These are sample questions; the exam has its own separate question set.

A statistical measure calculated from the population data is known as a ________.

A. Statistic
B. Parameter ✓
C. Standard Error
D. Bias

Answer: B. Parameter
A parameter is a characteristic value of the population (such as population mean or variance), whereas a statistic is calculated from sample data.

What is the formula for the Standard Error of the sample mean when sampling is done from an infinite population with population standard deviation σ?

A. σ / n
B. σ * √n
C. σ / √n ✓
D. √(σ / n)

Answer: C. σ / √n
The standard error of the sample mean (S.E.) for an infinite population or with-replacement sampling is given by σ / √n.

For a sample of size n = 100 drawn from a normal population with standard deviation σ = 15, what is the standard error of the sample mean?

A. 1.5 ✓
B. 0.15
C. 15.0
D. 0.015

Answer: A. 1.5
Standard Error (S.E.) = σ / √n = 15 / √100 = 15 / 10 = 1.5.

When testing a hypothesis about a single population mean with a small sample (n < 30), which of the following conditions strictly requires using the Student's t-test instead of the standard normal Z-test?

A. The population is non-normal and population variance is known.
B. The population is normal and population variance is known.
C. The population is normal and population variance is unknown. ✓
D. The sample is selected using non-probability sampling.

Answer: C. The population is normal and population variance is unknown.
Student's t-test is applied when the sample size is small (n < 30), the parent population is normal, and the population variance (σ²) is unknown, forcing the use of sample variance (s²).

A simple random sample of size n = 40 is drawn without replacement from a finite population of size N = 400. If the population variance is σ², which of the following expressions correctly represents the variance of the sample mean V(x-bar)?

A. σ² / 40
B. (σ² / 40) * (360 / 400)
C. (σ² / 40) * (360 / 399) ✓
D. (σ² / 40) * (359 / 399)

Answer: C. (σ² / 40) * (360 / 399)
For Simple Random Sampling Without Replacement (SRSWOR), the variance of the sample mean is V(x-bar) = (σ²/n) * ((N - n) / (N - 1)). Substituting n = 40 and N = 400 yields (σ²/40) * (360 / 399).

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