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Posttest

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Central Limit Theorem

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1: What does the Central Limit Theorem state about the sample mean?

a: The sample mean will always equal the population mean. Explanation

Explanation

b: The sample mean follows the same distribution as the population distribution. Explanation

Explanation

c: The distribution of the sample mean approaches a normal distribution as the sample size increases. Explanation

Explanation

d: The sample mean has a variance larger than the population variance. Explanation

Explanation

2: Which of the following conditions must be satisfied for the CLT to hold?

a: The population must be normally distributed. Explanation

Explanation

b: The sample size must be sufficiently large. Explanation

Explanation

c: The random variables must be independent and identically distributed (i.i.d.). Explanation

Explanation

d: Both b and c. Explanation

Explanation

3: If the population has a mean

\mu = 10

and variance

\sigma^2 = 4

, what is the variance of the sample mean for a sample size

n = 16

a: 4 Explanation

Explanation

b: 0.25 Explanation

Explanation

c: 1 Explanation

Explanation

d: 0.5 Explanation

Explanation

4: The Central Limit Theorem can be applied to which of the following scenarios?

a: Calculating the average weight of individuals in a city using a sample. Explanation

Explanation

b: Studying the variance of a single dataset with

n = 10

. Explanation

Explanation

c: Summing independent and identically distributed random variables. Explanation

Explanation

d: Both a and c. Explanation

Explanation

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