Sampling Distributions for Proportions and Means by David Spade, PhD

About the Lecture

The lecture Sampling Distributions for Proportions and Means by David Spade, PhD is from the course Statistics Part 2. It contains the following chapters:

Sampling distributions for proportions and means
Using the Normal Model for Proportions
The Central Limit Theorem
Illustrating the Normal Curve at Work

Included Quiz Questions

Which statement accurately describes a sampling distribution?

The sampling distribution refers to the distribution of the statistic calculated from many random samples of the same size.
The sampling distribution refers to the distribution of the individual values in a random sample.
The sampling refers to the value of the statistic obtained from one sample.
The sampling distribution and the distribution of individual values are the same for any sample size.
The sampling distribution refers to the standard deviation of the statistic calculated from many random samples of different sizes.

What is not one of the conditions necessary for the normal model to approximate the distribution of a sample proportion?

The sample size must be at least 10% of the population size.
The individuals in the sample must be independent of each other.
We must have an expectation of at least 10 successes.
We must have an expectation of at least 10 failures.
We must have at least 10 more successes than failures.

What is not true regarding the central limit theorem?

The central limit theorem requires that the population distribution is normal.
The central limit theorem states that the sampling distribution of the sample mean gets closer to the normal distribution as the sample size gets larger.
The central limit theorem relies on the assumption that our sample is drawn randomly.
The central limit theorem states that the variation in the sample mean is smaller than the variation in individual values.
The sample size must be smaller than 10% of the population size.

Consider a random sample of size 100 with a mean of 5 and a standard deviation of 10. What are the mean and the standard deviation of the distribution of the sample mean?

The mean is 5 and the standard deviation is 1.
The mean is 5 and the standard deviation is 10.
The mean is 5 and the standard deviation is 0.1.
The mean is 0 and the standard deviation is 1.
The mean is 100 and the standard deviation is 1.

What is true regarding the sampling distributions of means and proportions?

The use of the normal model as an approximation to the sampling distribution of the mean works well for small samples, provided that the underlying distribution looks fairly close to normal.
The use of the normal model as an approximation to the sampling distribution of the mean works well for small samples from highly skewed distributions.
The use of the normal model as an approximation to the sampling distribution of the mean or proportion works well even when the data is not independent.
The sampling distribution is the same as the distribution of the sample.
The use of the normal model as an approximation of the sampling distribution of the mean works best for medium-sized samples.

If the population size is 10,000 then what sample size is required to meet the 10% condition?