Questions: Choose the correct answer to complete the sentence: The spread of the estimated sampling distribution of x̄ is the spread of population of closing stock prices. less than the same as greater than

Choose the correct answer to complete the sentence:
The spread of the estimated sampling distribution of x̄ is the spread of population of closing stock prices.
less than
the same as
greater than

Transcript text: Choose the correct answer to complete the sentence: The spread of the estimated sampling distribution of $\bar{x}$ is $\qquad$ the spread of population of closing stock prices. less than the same as greater than

Solution

Solution Steps

To determine the relationship between the spread of the sampling distribution of $\bar{x}$ and the spread of the population, we need to understand that the spread of the sampling distribution (standard error) is generally less than the spread of the population (standard deviation) when the sample size is greater than one.

Step 1: Understanding the Spread of Distributions

The spread of the sampling distribution of the sample mean $\bar{x}$ is known as the standard error. It is calculated as $\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the standard deviation of the population and $n$ is the sample size.

Step 2: Comparing the Spreads

The standard deviation of the population is $\sigma$. The standard error $\frac{\sigma}{\sqrt{n}}$ is less than $\sigma$ when $n > 1$.

Step 3: Conclusion

Since the sample size is greater than one, the spread of the sampling distribution is less than the spread of the population.