STAT 5.5 sampling distribution

Front

What is a sampling distribution?

Back

A sampling distribution is the probability distribution of a statistic (like the sample mean or sample proportion) obtained from a large number of samples drawn from a specific population.

Front

What does the mean of a sampling distribution represent?

Back

The mean of a sampling distribution represents the average of all possible sample means or sample proportions from a population, and it is equal to the population parameter.

Front

What is the standard deviation of a sampling distribution called?

Back

The standard deviation of a sampling distribution is called the standard error.

Front

How do you calculate the standard error of the sample proportion?

Back

The standard error of the sample proportion (p̂) is calculated using the formula: SE = sqrt[(p(1-p)/n)], where p is the population proportion and n is the sample size.

Front

What is the Central Limit Theorem?

Back

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed if the sample size is sufficiently large, regardless of the population's distribution.

Front

What is the relationship between sample size and variability in sampling distributions?

Back

As the sample size increases, the variability (or spread) of the sampling distribution decreases, leading to a more accurate estimate of the population parameter.

Tags

CCSS.6.SP.A.2

Front

What does it mean if a sampling distribution is approximately normal?

Back

If a sampling distribution is approximately normal, it means that the distribution of sample means or proportions follows a bell-shaped curve, allowing for the use of normal probability methods.

Front

What is the significance of a sample proportion of 0.11 in a sampling distribution?

Back

A sample proportion of 0.11 indicates that, on average, 11% of the sampled population exhibits the characteristic of interest (e.g., being late to work) in repeated samples.

Front

How does the sample size affect the likelihood of observing extreme sample proportions?

Back

Smaller sample sizes tend to have more variability, making it more likely to observe extreme sample proportions compared to larger sample sizes, which are more stable.

Tags

CCSS.6.SP.A.2

Front

What is the formula for the mean of the sampling distribution of the sample proportion?

Back

The mean of the sampling distribution of the sample proportion is equal to the population proportion (p).