To determine which statement is NOT true regarding the sample mean from 100 independent and identically distributed (iid) observations, we would need to evaluate the provided statements, typically focusing on properties related to the sample mean, such as its expected value, variability, and distribution.

However, since you haven't provided the specific statements to analyze, I will outline the common properties of the sample mean that could help identify incorrect assertions:

1. **Expected Value**: The expected value of the sample mean is equal to the population mean.
2. **Variance**: The variance of the sample mean is equal to the population variance divided by the sample size (n), i.e., $ \text{Var}(\bar{X}) = \frac{\sigma^2}{n} $.
3. **Distribution**: With a sufficiently large sample size (like 100), the sample mean will be approximately normally distributed due to the Central Limit Theorem, regardless of the underlying population distribution.
4. **Convergence**: As the sample size increases, the sample mean will converge to the population mean.

With these principles in mind, please provide the specific statements, and I can indicate which one is NOT true.

Question

To determine which statement is NOT true regarding the sample mean from 100 independent and identically distributed (iid) observations, we would need to evaluate the provided statements, typically focusing on properties related to the sample mean, such as its expected value, variability, and distribution.

However, since you haven't provided the specific statements to analyze, I will outline the common properties of the sample mean that could help identify incorrect assertions:

1. **Expected Value**: The expected value of the sample mean is equal to the population mean.
2. **Variance**: The variance of the sample mean is equal to the population variance divided by the sample size (n), i.e., $ \text{Var}(\bar{X}) = \frac{\sigma^2}{n} $.
3. **Distribution**: With a sufficiently large sample size (like 100), the sample mean will be approximately normally distributed due to the Central Limit Theorem, regardless of the underlying population distribution.
4. **Convergence**: As the sample size increases, the sample mean will converge to the population mean.

With these principles in mind, please provide the specific statements, and I can indicate which one is NOT true.

Knowee AI · Accepted Answer

To determine which statement is NOT true regarding the sample mean from 100 independent and identically distributed (iid) observations, we would need to evaluate the provided statements, typically focusing on properties related to the sample mean, such as its expected value, variability, and distribution.

However, since you haven't provided the specific statements to analyze, I will outline the common properties of the sample mean that could help identify incorrect assertions:

1. **Expected Value**: The expected value of the sample mean is equal to the population mean.
2. **Variance**: The variance of the sample mean is equal to the population variance divided by the sample size (n), i.e., $ \text{Var}(\bar{X}) = \frac{\sigma^2}{n} $.
3. **Distribution**: With a sufficiently large sample size (like 100), the sample mean will be approximately normally distributed due to the Central Limit Theorem, regardless of the underlying population distribution.
4. **Convergence**: As the sample size increases, the sample mean will converge to the population mean.

With these principles in mind, please provide the specific statements, and I can indicate which one is NOT true.

Suppose we compute the sample mean from 100 iid observations. Which of the following is NOT true?

Question

Suppose we compute the sample mean from 100 iid observations. Which of the following is NOT true?

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