Question

10 words were picked at random from a story (our population) and the length of each is recorded below.

4, 1, 7, 1, 5, 4, 2, 7, 5, 5

1. Does this represent a sample or a resample of word lengths? Explain.

2. Regardless of your answer to part a., use the values collected and for each of the following, identify whether the word lengths represent a possible resample. For each that is not a possible resample, explain why.

1. A. 1, 1, 1, 2, 3, 4, 5, 7, 7, 7

1. B. 1, 1, 2, 2, 2, 2, 4, 5, 7, 7

1. C. 1, 1, 4, 4, 5, 5, 7, 7, 7, 7, 7

1. D. 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

3. The purpose of creating a bootstrap distribution is to: (select one)

A.   Estimate the mean of the unknown sampling distribution.
B.   Estimate the spread of the unknown sampling distribution.
C.   Both A and B.
D.   None of the above.

4. Indicate whether each statement is true or false.

A. The resample and original sample MUST be the same size.
B. The resample and original sample BOTH are taken from the population.
C.   The resample can ONLY use values that were in the original sample.
D. The resample uses ALL values that were in the original sample.

Answer 1

(a.) 4, 1, 7, 1, 5, 4, 2, 7, 5, 5

This represents a sample of word lengths.

As we know a sample is a smaller version of a large group means we take some of the random values from the population so that we can calculate inferences from data. It is a subset that contains the characteristics of a larger population.

Whereas, Resampling is used to estimate statistics on a population by sampling a dataset with replacement.

So, this is a sample as we are not creating a new resample from a sample itself by replacement.

(b.)

• A. 1, 1, 1, 2, 3, 4, 5, 7, 7, 7 - This is not a resample because it contains 3 which is not an element of our sample(4, 1, 7, 1, 5, 4, 2, 7, 5, 5) and for resample all elements should be from sample.

• B. 1, 1, 2, 2, 2, 2, 4, 5, 7, 7 - This is a resample. As all elements of this are from sample(4, 1, 7, 1, 5, 4, 2, 7, 5, 5) and size is the same as of the sample.

• C. 1, 1, 4, 4, 5, 5, 7, 7, 7, 7, 7- This is not a resample as it has got the size of 11 whereas sample size is 10 and size should be the same for resampling.

• D. 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 - This is a resample as the size is 10 and elements are from sample(4, 1, 7, 1, 5, 4, 2, 7, 5, 5).

(c.) option C - Both A and B.

(d.)

A - TRUE

B - FALSE (As the sample is taken from the population and resample is taken from the sample.)

C - TRUE

D - FALSE (As it can use all values or some of them.)