Sampling Distributions

Front

What is the mean of the sampling distribution of sample means (μ_x-bar) if the population mean (μ) is 794?

Back

μ_x-bar = 794

Front

What is the standard deviation of the sampling distribution of sample means (σ_x-bar) if the population standard deviation (σ) is 48 and the sample size (n) is 64?

Back

σ_x-bar = σ / √n = 48 / √64 = 6

Front

What conditions must be met to use the Normal Approximation for a sample proportion?

Back

Both np and n(1-p) must be at least 10.

Front

If 35% of US households have at least one dog, what is the probability that in a sample of 50 households, more than 50% own at least one dog?

Back

0.013

Front

What does the Central Limit Theorem (CLT) state about the sampling distribution of the sample mean?

Back

As the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Front

What is a Simple Random Sample (SRS)?

Back

A sample in which each member of the population has an equal chance of being selected.

Front

What is the formula for the standard error of the sample mean?

Back

Standard Error (SE) = σ / √n, where σ is the population standard deviation and n is the sample size.

Front

What is the difference between a population and a sample?

Back

A population includes all members of a specified group, while a sample is a subset of the population.

Front

What is the significance of the sample size (n) in determining the shape of the sampling distribution?

Back

Larger sample sizes lead to a sampling distribution that is more normally distributed, according to the Central Limit Theorem.

Front

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

Back

The mean of the sampling distribution (μ_x-bar) is equal to the population mean (μ).