Consider the following population: {24, 28, 32, 36}. Note that the population me
ID: 3133827 • Letter: C
Question
Consider the following population: {24, 28, 32, 36}. 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 are dispersed equally.They are both symmetric about the population mean.They both cover the same range.
In what ways are they different? (Select all that apply.)One distribution covers larger range.One distribution is more scattered than another.The distributions have different mean.
Explanation / Answer
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They are both symmetric about the population mean
One distribution covers larger range.One distribution is more scattered than another.The distributions have different mean.
Sample Sample Mean Sample Sample Mean 24, 28 26 32, 24 28 24, 32 29 32, 28 30 24, 36 30 32, 36 34 28, 24 26 36, 24 30 28, 32 30 36, 28 32 28, 36 32 36, 32 34