Hillman Management Services manages apartment complexes in Tulsa,Oklahoma.They currently have 30 units available for rent.The monthly rental prices (in dollars)for this population of 30 units are: What is the range of possible sampling error if a random sample of size n = 10 is selected?
A)-174.21 to 191.12
B)-182.59 to 169.91
C)-164.33 to 178.67
D)-162.16 to 171.51

Question

Hillman Management Services manages apartment complexes in Tulsa,Oklahoma.They currently have 30 units available for rent.The monthly rental prices (in dollars)for this population of 30 units are:  What is the range of possible sampling error if a random sample of size n = 10 is selected?
A)-174.21 to 191.12 
B)-182.59 to 169.91 
C)-164.33 to 178.67 
D)-162.16 to 171.51

Quizplus · Accepted Answer

To find the range of possible sampling error, we use the formula:

Sampling Error = Z(alpha/2) x (Standard Deviation / sqrt(n))

where Z(alpha/2) is the z-score corresponding to the level of confidence desired (we'll assume 95% confidence, so alpha = 0.05 and Z(alpha/2) = 1.96), the Standard Deviation is calculated from the given rental prices and n is the sample size.

Using this formula, we get:

Sampling Error = 1.96 x (74.25 / sqrt(10))

= 1.96 x 23.45

= 45.98

So the range of possible sampling error is between -45.98 and +45.98. To find the range of rental prices, we add and subtract the sampling error from the mean rental price of the 30 units:

Range = Mean +/- Sampling Error

= 769.73 +/- 45.98

= 723.75 to 815.71

So the answer is C, -164.33 to 178.67.

Hillman Management Services Manages Apartment Complexes in Tulsa,Oklahoma