Worksheet 24: Sampling bias#
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Practice quiz 2#
Decide whether the following statement is True or False, and justify your answer: “When estimating a mean, a larger sample size will make the confidence interval smaller.”
In the following scenario, explain
a. What is the population
b. What is the variable \(x\) being measured
c. What is the sample \(x_1,\ldots,x_n\)
A penguin ecologist is trying to determine the average number of offspring a female Antarctic penguin will hatch over her lifetime. The ecologist tags \(n\) Antarctic female penguins at random, then records the number of eggs that each penguin hatches in her lifetime.
Suppose you conduct a poll on an issue on which the population is roughly divided. You survey \(n=50\) people and 20 said yes.
a. Compute \(\hat{\pi}_n\) the sample proportion of people who said yes.
b. Suppose that the standard deviation of \(\hat{\pi}_n\) is \(0.07\). Construct a 95% confidence interval for \(\pi\) the proportion of people in the population who would say yes.
How would your answer to question 3 change if you were asked for a 99% interval instead?
How would your answer change if your were told \(\hat{\sigma}_x\) (the sample standard deviation of \(x_1,\ldots,x_n\)) instead of the standard deviation of the estimate?
Gettysburg address#
Four score and seven years ago our fathers brought forth on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal. Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battlefield of that war. We have come to dedicate a portion of that field, as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this. But, in a larger sense, we can not dedicate – we can not consecrate – we can not hallow – this ground. The brave men, living and dead, who struggled here, have consecrated it, far above our poor power to add or detract. The world will little note, nor long remember what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us – that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion – that we here highly resolve that these dead shall not have died in vain – that this nation, under God, shall have a new birth of freedom – and that government of the people, by the people, for the people, shall not perish from the earth.
Sample ten words from the Gettysburg address and write them down:
Sampling bias#
What could be causing the bias when sampling words?
How could using college students bias the results of studies?
Can you think of other examples of survivorship bias?