A realtor has 20 residential listings under contract. The following table shows

Question

A realtor has 20 residential listings under contract. The following table shows the number of days each of these 20 houses has been on the market as of today. Use the data to complete parts a through d below. 21 24 3 16 32 24 42 54 52 22 42 55 49 11 45 10 39 65 24 73 a. Calculate mean for this population. mu = 35.15 (Type an integer or a decimal.) b. Calculate the sampling error using the first 5 homos in the first row as your sample. The sampling error for the first 5 homes is. (Type an integer or a decimal.) c. Calculate the sampling error using all 10 homes in the first row as your sample. The sampling error for the first 10 homes is. (Type an integer or a decimal.) d. How does increasing the sample size affect the sampling error? A. In general, increasing the sample size has no effect on the sampling error. B. In general, increasing the sample size makes the sampling error larger. C. In general, increasing the sample size makes the sampling error smaller.

Explanation / Answer

The general formula for the margin of error for a sample proportion (if certain conditions are met) is

Z*{p(1-p)/n}

where

p is the sample proportion, n is the sample size, and z* is the appropriate z*-value for your desired level of confidence (from the following table).

z*-Values for Selected (Percentage) Confidence
Levels

2.58.

So b) here p=5/20=.25

So for 95% confidence of interval sampling error is 1.96*{(.25*.75)/20}=.1897

So 19 plus or minus sampling error with 95% confidence interval

For c) p=10/20=.5

So for 95% confidence of interval sampling error is 1.96*{(.5*.5)/20=0.219

Here 22 plus or minus sampling error with 95% confidence interval.

Percentage Confidence z*-Value 80 1.28 90 1.645 95 1.96 98 2.33 99

2.58.

So b) here p=5/20=.25

So for 95% confidence of interval sampling error is 1.96*{(.25*.75)/20}=.1897

So 19 plus or minus sampling error with 95% confidence interval

For c) p=10/20=.5

So for 95% confidence of interval sampling error is 1.96*{(.5*.5)/20=0.219

Here 22 plus or minus sampling error with 95% confidence interval.

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