Central Limit Theorem

What is the relationship between the mean of the population and the mean of the sampling distribution of the sample means?

• the mean of the population is greater than the mean of the sampling distribution of the sample means.

• the mean of the population is lesser than the mean of the sampling distribution of the sample means.

• the mean of the population is equal to the mean of the sampling distribution of the sample means.

• the mean of the population is not equal to the mean of the sampling distribution of the sample means.

Tags

CCSS.HSS.IC.A.1

What is the equivalent value of the standard deviation of the sampling distribution of the sample means in comparison to the standard deviation in an infinite population?

• 
• 

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

What is the equivalent value of the standard deviation of the sampling distribution of the sample means in comparison to the standard deviation in a finite population?

• 
• 

Tags

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

In the formula shown above, what does N stands for?

• sample size

• population size

• number of respondents

• number 30

Tags

CCSS.HSS.IC.A.1

What have you observed with the histogram of the sampling distribution of the sample mean?

• The histogram is skewed to the left, regardless of the shape of the population.

• It will tend to have an abnormal distribution, regardless of the shape of the population.

• The bar in the histogram will be equally distributed

• It will tend to have a normal distribution, regardless of the shape of the population.

Tags

CCSS.HSS.ID.A.1

CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.3

CCSS.HSS.ID.A.4

According to the Central Limit Theorem, For a sample to be large enough, the sample size should be ______.

• half of the population

• 75% of the population size

• at least 30

• at most 100

Which of the following symbol describes the population mean?

• $\mu$

• $n$

• $x̄$

• $σ$

Which of the following symbol describes the population standard deviation?

• $\mu$

•  $s$  
  

• $x̄$

• $σ$

Tags

CCSS.HSS.ID.A.4

Consider a population with  $\mu=50$  and  $\sigma=5$ is taken. Find the mean of the sampling distribution of the sample mean with a sample size of 30.

• 50

• 25

• 20

• 5

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

Consider a population with  $\mu=50$  and  $\sigma=5$ is taken. Find the standard deviation of the sampling distribution of the sample mean with a sample size of 30.

• 5

• 0.91

• 0.71

• 0

Tags

CCSS.HSS.ID.A.4