Sampling Distributions and Standard Error

The video tutorial explains the concept of sampling distributions, differentiating them from sample and population distributions. It covers the central limit theorem, the calculation of standard deviation and standard error, and the importance of sampling distributions in statistical analysis. The video also includes practice questions to reinforce understanding.

What is the main difference between a sample distribution and a sampling distribution?

• A sample distribution has less variability than a sampling distribution.

• A sample distribution is always normally distributed, while a sampling distribution is not.

• A sample distribution is based on a single sample, while a sampling distribution uses multiple samples.

• A sample distribution uses multiple samples, while a sampling distribution uses one.

What is the first step in creating a sampling distribution?

• Determine the standard deviation of the sample.

• Plot the histogram of the population.

• Select a random sample of size n.

• Calculate the mean of the population.

How does the standard deviation of a sampling distribution compare to that of a population distribution?

• It varies depending on the sample size.

• It is always larger.

• It is always smaller.

• It is the same.

Why is a sampling distribution useful in practical applications?

• It requires measuring every individual in the population.

• It provides an exact value of the population mean.

• It allows estimation of the population mean without measuring everyone.

• It eliminates the need for statistical analysis.

What is the probability that the average height of 10 random Canadians is less than 157 cm?

• 0.0764

• 0.9236

• 0.0869

• 0.5

What is the standard error if the population standard deviation is 7 and the sample size is 10?

• 2.21

• 7

• 0.7

• 10

What is the z-score for a sample mean of 157 when the population mean is 160 and the standard error is 2.21?

• 0

• -1.36

• 2.21

• 1.36

What is the proportion of all people with heights greater than 170 cm?

• 0.0764

• 0.9236

• 0.0869

• 0.5

Which distribution is used when calculating the probability of a sample mean?

• Population distribution

• Sample distribution

• Sampling distribution

• Normal distribution

What is the total area under a normal distribution curve?

• 0.9236

• 2

• 1

• 0.5