Sampling Distributions and Estimators

The video tutorial covers key concepts in sampling distribution, including the role of the mean and variability in normal distributions. It explains the concept of an unbiased estimator and how sample size affects variability. The tutorial also discusses the practical consequences of changing sample sizes and the importance of minimizing bias and variability in statistical estimates.

What is the center of a normal distribution?

• The mean

• The range

• The median

• The mode

What does the standard deviation in a normal distribution indicate?

• The average value

• The spread of the data

• The highest value

• The lowest value

What is an unbiased estimator?

• A statistic whose mean equals the parameter being estimated

• A statistic that always overestimates the parameter

• A statistic that always underestimates the parameter

• A statistic that is not related to the parameter

In the example given, what is the true population maximum?

• 150

• 100

• 75

• 50

Which sampling distribution is more likely to be an unbiased estimator?

• A distribution with no clear pattern

• A roughly symmetric distribution

• A distribution skewed to the right

• A distribution skewed to the left

Why are larger sample sizes preferred?

• They decrease variability

• They increase variability

• They make calculations easier

• They are more expensive

What happens to sampling variability when the sample size increases?

• It increases

• It decreases

• It remains the same

• It becomes unpredictable

What is the effect of decreasing the sample size from 100 to 50?

• The sampling distribution becomes less variable

• The sampling distribution becomes more precise

• The sampling distribution becomes more variable

• The sampling distribution remains unchanged

What is a practical consequence of increased variability in estimates?

• Estimates become less important

• Estimates are closer to the true value

• Estimates become more accurate

• Estimates are farther from the true value

What does high bias in sample statistics indicate?

• Sample values are centered on the population value

• Sample values consistently miss the target in the same direction

• Sample values are randomly distributed

• Sample values are always accurate