Chapter Exam

Chapter 2: Tests Based on Sampling Distributions - I — Online MCQ Test

Q: Which distribution is used for small-sample test of a single population mean when population standard deviation is unknown?

Answer: B. t-distribution — For small samples with unknown population standard deviation, the Student's t-distribution is used to test the population mean.

Q: The degrees of freedom for a one-sample t-test with sample size n is

Answer: C. n - 1 — In a one-sample t-test, one parameter is estimated from the sample, so degrees of freedom become n - 1.

Q: A sample of size 16 has mean 52 and sample standard deviation 8. The null hypothesis is H0: μ = 50. Which test statistic is correct?

Answer: A. (52 - 50) / (8 / 4) — For a one-sample t-test, the statistic is t = (x̄ - μ0) / (s/√n). Here, s/√n = 8/4.

Q: A researcher compares the marks of students before and after coaching using the same group of students. Which test is appropriate?

Answer: B. Paired t-test — Because the same students are measured twice, the observations are dependent, so a paired t-test is suitable.

Q: In a right-tailed chi-square test for variance, the rejection region lies in the

Answer: B. right tail — A right-tailed test rejects the null hypothesis when the chi-square statistic is sufficiently large, so the rejection region is in the right tail.

STATISTICS · CLASS 12th · Tamil Nadu State Board

Practice Chapter 2: Tests Based on Sampling Distributions - I with a free chapter-wise online MCQ test for Tamil Nadu State Board CLASS 12th STATISTICS. This chapter covers: Focusing on exact small sample tests this chapter details student t-distribution and chi-square distribution principles. Students learn test procedures for single mean difference b.... AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 2: Tests Based on Sampling Distributions - I — Important Questions & Answers (FAQ)

Frequently asked questions from Tamil Nadu State Board CLASS 12th STATISTICS — Chapter 2: Tests Based on Sampling Distributions - I, with answers and explanations. These are sample questions; the exam has its own separate question set.

Which distribution is used for small-sample test of a single population mean when population standard deviation is unknown?

A. Normal distribution
B. t-distribution ✓
C. Chi-square distribution
D. F-distribution

Answer: B. t-distribution
For small samples with unknown population standard deviation, the Student's t-distribution is used to test the population mean.

The degrees of freedom for a one-sample t-test with sample size n is

A. n
B. n + 1
C. n - 1 ✓
D. 2n - 1

Answer: C. n - 1
In a one-sample t-test, one parameter is estimated from the sample, so degrees of freedom become n - 1.

A sample of size 16 has mean 52 and sample standard deviation 8. The null hypothesis is H0: μ = 50. Which test statistic is correct?

A. (52 - 50) / (8 / 4) ✓
B. (50 - 52) / (8 / 16)
C. (52 - 50) / (8 / 16)
D. (52 - 50) / 8

Answer: A. (52 - 50) / (8 / 4)
For a one-sample t-test, the statistic is t = (x̄ - μ0) / (s/√n). Here, s/√n = 8/4.

A researcher compares the marks of students before and after coaching using the same group of students. Which test is appropriate?

A. Two-sample z-test
B. Paired t-test ✓
C. Chi-square test for variance
D. Correlation test

Answer: B. Paired t-test
Because the same students are measured twice, the observations are dependent, so a paired t-test is suitable.

In a right-tailed chi-square test for variance, the rejection region lies in the

A. left tail
B. right tail ✓
C. both tails equally
D. middle of the distribution

Answer: B. right tail
A right-tailed test rejects the null hypothesis when the chi-square statistic is sufficiently large, so the rejection region is in the right tail.