Answer-first summary for fast verification
Answer: Statement I is correct and Statement II is incorrect.
**Explanation:** **Statement I is correct:** The t-distribution is indeed similar to the normal distribution but has fatter tails. This means it has more probability in the tails compared to the normal distribution, which makes it appropriate for smaller sample sizes where the population standard deviation is unknown. **Statement II is incorrect:** While it's true that degrees of freedom for the t-distribution are equal to n - 1 (where n is the sample size), the second part of the statement is wrong. Actually: 1. The t-distribution approaches the normal distribution as degrees of freedom **increase** (not decrease) 2. Confidence intervals become **narrower** when degrees of freedom are greater (which is correct in the statement), but this happens because with larger sample sizes, we have more information and thus more precise estimates The t-distribution with low degrees of freedom has fatter tails and is more spread out than the normal distribution. As degrees of freedom increase, the t-distribution converges to the normal distribution.
Author: Nikitesh Somanthe
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Q.3280 Which of the following statement(s) are accurate?
I. The t-distribution is similar but not identical to the normal distribution in shape. It has fatter tails compared to the normal distribution. II. Degrees of freedom for the t-distribution is equal to n - 1. Students' t-distribution is closer to a normal distribution when the degrees of freedom are lower, and the confidence intervals are narrower when the degree of freedom is greater.
A
Statement I is correct and Statement II is incorrect.
B
Statement I and Statement II are both correct.
C
Statement I and Statement II are both incorrect.
D
Statement I is incorrect and Statement II is correct.