PS_9.6.1 Video Lesson - Intro to Central Limit Theorem

What is the process of creating a sampling distribution?

• Taking a single sample from a population and calculating its mean.

• Repeatedly taking samples from a population, calculating a statistic for each, and combining this information into a distribution.

• Analyzing the entire population to determine its mean and standard deviation.

• Randomly selecting data points from a single sample to form a new distribution.

What does the Central Limit Theorem predict about the shape of the sampling distribution of the sample mean when the sample size is sufficiently large?

• It will always be skewed, regardless of the original population distribution.

• It will resemble the shape of the original population distribution.

• It will be approximately normal, regardless of the original population distribution's shape.

• It will become bimodal if the original population distribution is also bimodal.

What is the generally accepted minimum sample size for the Central Limit Theorem to be safely applied, ensuring the sampling distribution of the sample mean is approximately normal?

• n < 15

• n > 20

• n > 30

• n = 100

Tags

CCSS.HSS.ID.A.4

In which scenario can the Central Limit Theorem still be applied to produce an approximately normal sampling distribution, even if the sample size is less than 30?

• When the population distribution is heavily skewed.

• When the population distribution is already normally distributed.

• When the population is very small.

• When the data points are categorical.

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population

• The sample

• The sampling distribution (mean)

• The sampling distribution (proportion)

As n gets smaller → the sampling distribution of the sample mean (𝑥̅) looks more normal and bell shaped

• True

• False

To be able to apply the Central Limit Theorem, which of the following is true in regards of how large n has to be?

• If the distribution of the X is skewed, then a sample size n of at least 30 yields an adequate approximation.

• If the distribution of the X is slightly skewed, then a sample size n of at least 25 or 30 yields an adequate approximation.

• If the distribution of the X is extremely skewed, then a sample size n of greater than 30 yields an adequate approximation.

Tags

CCSS.HSS.ID.A.4

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.6.SP.A.2

• 50

• 25

• 20

• 5

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

• 534.7

• 26.2

• 40

• 4.14