Consider measuring the time until death after diagnosis of a particular disease, and suppose that we have complete follow up, so that all death times are observed. We will assume the following to be known values for the population. We know that the mean time until death after diagnosis is 6.5 years. We also know that the standard deviation of time until death is 4.1 years. Further, we know that the distribution of time until death is very strongly skewed to the right (positively skewed) for this population. Use this to answer the following.

Part (a) ( WebWorkiR ) Suppose that we take a simple random sample of 15 people from this population. What would we 'expect' our sample mean to be for our sample of 15 individuals? That is, what is the expected value of the sample mean?

A. It depends on the sample size
B. Greater than 6.5
C. Less than 6.5
D. Exactly equal to 6.5


Part (b) ( WebWorkiR ) Suppose that we take a simple random sample of 15 people from this population. What would we 'expect' our sample standard deviation to be for our sample of 15 individuals? That is, what is the expected value of the sample standard deviation?

A. Exactly equal to 4.1
B. It depends on the sample size
C. Less than 4.1
D. Greater than 4.1


Part (c) ( WebWorkiR ) If we made a histogram of these 10 observations, what shape would we 'expect' this histogram to have?

A. Normally distributed
B. Skewed to the left
C. Symmetric
D. Skewed to the right
E. It depends on the sample size


Part (d) ( WebWorkiR ) Suppose that we take a simple random sample of 150 people from this population. What would we 'expect' our sample mean to be for our sample of 150 individuals? That is, what is the expected value of the sample mean?

A. Greater than 6.5
B. Exactly equal to 6.5
C. It depends on the sample size
D. Less than 6.5


Part (e) ( WebWorkiR ) Suppose that we take a simple random sample of 150 people from this population. What would we 'expect' our sample standard deviation to be for our sample of 150 individuals? That is, what is the expected value of the sample standard deviation?

A. Less than 4.1
B. It depends on the sample size
C. Greater than 4.1
D. Exactly equal to 4.1


Part (f) ( WebWorkiR ) If we made a histogram of these 150 observations, what shape would we 'expect' this histogram to have?

A. Skewed to the left
B. Symmetric
C. It depends on the sample size
D. Normally distributed
E. Skewed to the right


Part (g) ( On-Paper ) Again, consider taking a sample of 150 observations from this population. In a few sentences (you are encouraged to use pictures or notation if this helps), explain what is mean by the term "The Sampling Distribution of The Sample Mean", in the context of this example. In your explanation, imagine that you are explaining to a friend with limited understanding of statistics, and avoid the use of technical terms as much as possible. Also, please state any assumptions that are relevant to your description of the sampling distribution.