Chapter 6, Section 1-CI, Exercise 030 LINK TO TEXT Chapter 6, Section 1-CI, Exer
ID: 3363433 • Letter: C
Question
Chapter 6, Section 1-CI, Exercise 030
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Chapter 6, Section 1-CI, Exercise 030
Standard Error from a Formula and a Bootstrap Distribution
Use StatKey or other technology to generate a bootstrap distribution of sample proportions and find the standard error for that distribution. Compare the result to the standard error given by the Central Limit Theorem, using the sample proportion as an estimate of the population proportion p.
Proportion of lie detector trials in which the technology misses a lie, with n=43 and p^=0.361
Click here to access StatKey.
Round your answer for the bootstrap SE to two decimal places, and your answer for the formula SE to three decimal places.
Bootstrap SE=
Formula SE=
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Explanation / Answer
Using StatKey or other technology to create a bootstrap distribution, we see for one set of 1000 simulations that SE = 0.073. (Answers may vary slightly with other simulations.) Using the formula from the Central Limit Theorem, and using ˆp = 0.361 as an estimate for p, we have
SE = Sqrt p(1 p)/ n sqrt 0.361(1 0.361) / 43 = 0.073
We see that the bootstrap standard error and the formula match very closely.