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Chapter 7: Q1 (page 342)

Replacement

Why does the bootstrap method require sampling with replacement? What would happen if we used the methods of this section but sampled without replacement?

Short Answer

Expert verified

If the sampling is done with replacement, it can be repeatedly picked in subsequent draws.

If sampling is done without replacement, the confidence interval for a bootstrapped sample is not going to work because all the samples are going to have the same summary statistics.

Step by step solution

01

Describe the concept of the bootstrap sample

A bootstrap sample is a sample obtained from another randomly selected sample.

Thus, a resampling method where large numbers of smaller samples of the same size are repeatedly drawn with replacement from a single original sample is bootstrapping.

02

State the reason of bootstrap method requires sampling with replacement

The bootstrap samples are the same size as the original data set. If sampling is done with replacement, then a large number of smaller samples of the same size are repeatedly drawn to ensure that an appropriate confidence interval can be constructed.

03

Explain the bootstrap sampling method under without replacement

If sampling is done without replacement, it would end up with the same data over and over.

Therefore, the means or standard deviation or proportions, or variance would be the same for the original sample and bootstrap sample.

Hence, the confidence interval for the bootstrapped sample is not going to work because all of those samples are going to have the same summary statistics.

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Most popular questions from this chapter

In Exercises 1鈥�3, refer to the accompanying screen display that results from the Verizon airport data speeds (Mbps) from Data Set 32 鈥淎irport Data Speeds鈥� in Appendix B. The confidence level of 95% was used.

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Finite Population Correction Factor For Formulas 7-2 and 7-3 we assume that the population is infinite or very large and that we are sampling with replacement. When we sample without replacement from a relatively small population with size N, we modify E to include the finite population correction factor shown here, and we can solve for n to obtain the result given here. Use this result to repeat part (b) of Exercise 38, assuming that we limit our population to a county with 2500 women who have completed the time during which they can give birth.

E=z伪2p^q^nN-nN-1

n=Np^q^z伪22p^q^z伪22+N-1E2

Caffeine in Soft Drinks Listed below are measured amounts of caffeine (mg per 12oz of drink) obtained in one can from each of 20 brands (7UP, A&W root Beer, Cherry Coke, 鈥aB). Use a confidence interval 99%. Does the confidence interval give us good information about the population of all cans of the same 20 brands that are consumed? Does the sample appear to be from a normally distributed population? If not, how are the results affected?

0 0 34 34 34 45 41 51 55 36 47 41 0 0 53 54 38 0 41 47
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