P&S: Central Limit Theorem

Front

What is the Central Limit Theorem?

Back

The Central Limit Theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the population's distribution, provided the sample size is sufficiently large (usually n ≥ 30).

Front

What is the mean of the sampling distribution?

Back

The mean of the sampling distribution is equal to the mean of the population from which the samples are drawn.

Front

What is the standard error of the mean?

Back

The standard error of the mean (SEM) is the standard deviation of the sampling distribution of the sample mean, calculated as the population standard deviation divided by the square root of the sample size (SEM = σ/√n).

Front

How do you calculate the standard error if the population standard deviation is 40 and the sample size is 25?

Back

Standard Error (SE) = σ/√n = 40/√25 = 40/5 = 8.

Front

What is the purpose of using a random sampling method?

Back

The purpose of using a random sampling method is to reduce bias in the selection of samples, ensuring that every member of the population has an equal chance of being included.

Front

What does the 90th percentile represent in a normally distributed population?

Back

The 90th percentile represents the value below which 90% of the observations fall.

Front

If a population has a mean of 15.8 years and a standard deviation of 0.6 years, what age represents the 90th percentile?

Back

The age that represents the 90th percentile is approximately 16.569 years.

Front

What symbols represent the mean and standard deviation for a population?

Back

The symbols μ (mu) for mean and σ (sigma) for standard deviation represent the population parameters.

Front

What is the relationship between sample size and the standard error?

Back

As the sample size increases, the standard error decreases, leading to a more precise estimate of the population mean.

Front

What is a sampling distribution?

Back

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