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Homework answers / question archive / 1)Sampling a population is often necessary because the cost of studying all the items in the population is prohibitive
1)Sampling a population is often necessary because the cost of studying all the items in the population is prohibitive.
2.
Human Resource Consulting (HRC) surveyed a random sample of 60 Twin Cities construction companies to find information on the costs of their health care plans. One of the items being tracked is the annual deductible that employees must pay. The Minnesota Department of Labor reports that historically the mean deductible amount per employee is $502 with a standard deviation of $100. 
a. 
Compute the standard error of the sample mean for HRC. 
b. 
What is the chance HRC finds a sample mean between $477 and $527? 
c. 
Calculate the likelihood that the sample mean is between $492 and $512. 
d. 
What is the probability the sample mean is greater than $550? 
3.
Given below are the last four digits of 18 random phone numbers of your local population. 






3,138 
3,898 
4,498 
9,443 
5,319 
9,223 
2,366 
1,001 
3,653 
4,895 
5,819 
3,135 
6,201 
9,585 
5,022 
4,322 
9,856 
4,128 

Fill in the frequency table of the final digit of 18 randomly selected phone numbers. 
Digit 
Frequency 
0 
0 
1 
2 
2 
2 
3 
3 
4 
0 
5 
3 
6 
2 
7 
0 
8 
4 
9 
2 

Using the sample mean of the final four digits (9704 would lead to a mean of 5), compute the mean of the sample means. 

Given below are the last four digits of 18 random phone numbers of your local population. 






3,138 
3,898 
4,498 
9,443 
5,319 
9,223 
2,366 
1,001 
3,653 
4,895 
5,819 
3,135 
6,201 
9,585 
5,022 
4,322 
9,856 
4,128 

Fill in the frequency table of the final digit of 18 randomly selected phone numbers. 
Digit 
Frequency 
0 

1 

2 

3 

4 

5 

6 

7 

8 

9 


Using the sample mean of the final four digits (9704 would lead to a mean of 5), compute the mean of the sample means. 

4.
The Quality Control Department employs five technicians during the day shift. Listed below is the number of times each technician instructed the production foreman to shut down the manufacturing process last week. 
Technician 
Shutdowns 
Taylor 
3 
Hurley 
2 
Gupta 
4 
Rousche 
5 
Huang 
4 

a. 
How many samples, without replacement, of size two are possible? 


b. 
Compute the mean of the sample means and compare it to the population mean. 




The mean of the sample means is 
3.6 
The population mean is 
3.6 

5.
We can expect some difference between sample statistics and the corresponding population parameters. This difference is called the sampling error.
6.
A population consists of the following five values: 12, 12, 14, 15, and 20. 

a. 
List all samples of size 3, and compute the mean of each sample. 


b. 
Compute the mean of the distribution of sample means and the population mean 


7.
All possible samples of size n are selected from a population and the mean of each sample is determined. What is the mean of the sample means?
8.
For a distribution of sample means constructed by sampling 5 items from a population of 15, ___________.
9.
According to the central limit theorem, ____________.
10.
To study the population of consumer perceptions of new technology, sampling of the population is preferred over surveying the population because _________.
11.
When dividing a population into subgroups so that a random sample from each subgroup can be collected, what type of sampling is used?
12.
Manufacturers were subdivided into groups by volume of sales. Those with more than $100 million in sales were classified as large; those from $50 to $100 million as medium size; and those between $25 and $50 million, and so on. Samples were then selected from each of these groups. What is this type of sampling called?
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