sampling
Copyright 2010 Graham Elliott. All Rights Reserved.
Sampling
We are now putting all of the pieces together. Considering each observation xi as an outcome from a random variable Xi , we have that functions g(x1 ; x2 ; :::; xn ) are draws from the random variable
Pn g(X1 ; X2 ; :::; Xn ):
For 120a the function we are interested in is the sample mean — g(x1 ; x2 ; :::; xn ) = n1 i=1 xi : In this chapter we work with this function for distributions with many random variables.
1
From the Text
Question 1. Problem 6-10, p.206
Question 2: Problems 6-16,6-22.
Question 3: Problem 6-36.
2
Sampling Questions
Question 1. A study suggests that in a trial of 50 people the average decrease in cholestorol from using a particular drug is 18 points with a standard deviation of 10 points.
(a) What is the chance that, given the true e¤ect is a reduction of 20 points, that a particular person has no decrease in cholestorol when they take this drug?
(b) A reporter writes a newspaper article discussing the drug. They report that although the study claims that the reduction is 18 points, they have found a user that actually had no change to their cholestorol. They use this persons story to argue that the results are misleading. What is the chance that, if the real e¤ect was zero, that the average in a trial might be 18 just by chance?
(c) Is the counter example found by the reporter useful in understanding the results for the study?
Question 2. In the questions on normal probabilities, we examined probabilities of di¤erent ages where people marry. We wish to see if the data really supports a mean of 26 years (and standard deviation of 4 years) for …rst marriage. We collect a random sample of 100 people and record what age they were when they …rst married. We …nd that the mean of our sample is 28 years.
(a)
What is the chance that if the mean really were 26 years we would obtain a sample with a mean of 28 years or higher?
(b)
Do you believe that the true mean could be 26 years?
Sampling
We are now putting all of the pieces together. Considering each observation xi as an outcome from a random variable Xi , we have that functions g(x1 ; x2 ; :::; xn ) are draws from the random variable
Pn g(X1 ; X2 ; :::; Xn ):
For 120a the function we are interested in is the sample mean — g(x1 ; x2 ; :::; xn ) = n1 i=1 xi : In this chapter we work with this function for distributions with many random variables.
1
From the Text
Question 1. Problem 6-10, p.206
Question 2: Problems 6-16,6-22.
Question 3: Problem 6-36.
2
Sampling Questions
Question 1. A study suggests that in a trial of 50 people the average decrease in cholestorol from using a particular drug is 18 points with a standard deviation of 10 points.
(a) What is the chance that, given the true e¤ect is a reduction of 20 points, that a particular person has no decrease in cholestorol when they take this drug?
(b) A reporter writes a newspaper article discussing the drug. They report that although the study claims that the reduction is 18 points, they have found a user that actually had no change to their cholestorol. They use this persons story to argue that the results are misleading. What is the chance that, if the real e¤ect was zero, that the average in a trial might be 18 just by chance?
(c) Is the counter example found by the reporter useful in understanding the results for the study?
Question 2. In the questions on normal probabilities, we examined probabilities of di¤erent ages where people marry. We wish to see if the data really supports a mean of 26 years (and standard deviation of 4 years) for …rst marriage. We collect a random sample of 100 people and record what age they were when they …rst married. We …nd that the mean of our sample is 28 years.
(a)
What is the chance that if the mean really were 26 years we would obtain a sample with a mean of 28 years or higher?
(b)
Do you believe that the true mean could be 26 years?