Consider the following population: {1, 5, 9, 13}. Note that the population mean

Question

Consider the following population: {1, 5, 9, 13}. Note that the population mean is the following.

Compute the sample mean for each of the 12 possible samples.

Use this information to construct the sampling distribution of x. (Display the sampling distribution as a density histogram.)

Use the histogram to complete the table. (Enter the probabilities as fractions.)

(b) Suppose that a random sample of size 2 is to be selected, but this time sampling will be done with replacement. Using a method similar to that of Part (a), construct the sampling distribution of x. Hint: There are 16 different possible samples in this case. (Enter the probabilities as fractions.)

Use the histogram to complete the table.

(c) In what ways are the two sampling distributions of Parts (a) and (b) similar? (Select all that apply.)

They both cover the same range.They are both symmetric about the population mean.They are dispersed equally.

In what ways are they different? (Select all that apply.)The distributions have different mean.One distribution is more scattered than another.One distribution covers larger range.

1, 5 1, 9 1, 13 5, 1 5, 9 5, 13 9, 1 9, 5 9, 13 13, 1 13, 5 13, 9

Explanation / Answer

1 5 9 13

1 3 5 7 3 5 7 9 5 7 9 11 7 9 11 13

  

c)

In what ways are the two sampling distributions of Parts (a) and (b) similar?

They are both symmetric about the population mean.

In what ways are they different?

One distribution covers larger range.

Sample Sample Mean Sample Sample Mean 1, 5 3 9, 1 5 1, 9 5 9, 5 7 1, 13 7 9, 13 11 5, 1 3 13, 1 7 5, 9 7 13, 5 9 5, 13 9 13, 9 11

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