Chapter 2: Tests Based on Sampling Distributions - I — Online MCQ Test
STATISTICS · CLASS 12th · Tamil Nadu State Board
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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....
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Chapter 2: Tests Based on Sampling Distributions - I — Important Questions & Answers
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.
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.
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.
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.
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.
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.