Project #15392 - Stat

 

 

 
 
  • Description

    Homework 8 deals with confidence intervals for a population proportion p. Topics include calculating and interpreting confidence intervals, and determining the sample size needed for a specified level of confidence and margin of error.

 
 
 
 

Many people consider themselves "green", meaning they are supportive (in theory) when it comes to environmental issues. But are people willing to "put their money where their mouth is"?

For more than 30 years the National Opinion Research Center at the University of Chicago (www.norc.uchicago.edu) has conducted every year or every other year an opinion survey called the General Social Survey (GSS). The survey randomly samples 2000 adult Americans and asks each person a long list of questions in a 90-minute in-person interview.

In 2006 the GSS asked subjects whether they would be willing to pay higher prices in order to protect the environment. The data were collected under the variable GRNPRICE. To see the survey results on GRNPRICE, go to the GSS web site and do the following:

  • Click on "GSS - with 'no weight' as the default weight selection"
  • In the right column under SDA Frequencies/Crosstabulation Program, in the Row area type GRNPRICE
  • Click the Run the Table button at the bottom of the right column
  • In the Frequency Distribution table you should see the number of responses and percentage of responses in each of 5 categories; at the bottom in COL TOTAL is the total for the 5 categories.

Question 1. Calculate a 95% confidence interval for the proportion p of adult Americans that are very willing or fairly willing (add the responses in these two categories) at the time of the survey to pay higher prices to protect the environment.

lower bound (use 3 decimal places)
upper bound (use 3 decimal places)

Question 2. The GSS also asked subjects whether it should or should not be the government's responsibility to impose strict laws to make industry do less damage to the environment. The data were collected under the variable GRNLAWS. Follow the steps above Question 1 to access the results for the variable GRNLAWS and construct a 95% confidence interval for the proportion p of adult Americans that think it definitely should be or probably should be the government's responsibility to impose strict laws to make industry do less damage to the environment.

lower bound (use 3 decimal places)
upper bound (use 3 decimal places).
 
 
Question Part
Points
Submissions Used
1 2 3
/1 /1 /1
0/4 0/4 0/4
Total
/3
 

Your employer, Apricot Computers, Inc., is interested in locating a new manufacturing facility in North Carolina. For easier access to their markets along the East coast and in the Atlanta area Apricot would like to locate the facility in the vicinity of Interstate 85.

Since Apricot is also interested in the educational level of the local workforce in the locations under consideration, you are told to obtain an estimate p^^\^ of the proportion p of the population over age 25 with a bachelors degree in each of several counties in the vicinity of Interstate 85, and present your results to the Apricot CEO.

To enhance your presentation to the CEO, you would like to show a plot of your estimates on a map of North Carolina. The data that you collected for 12 North Carolina counties in the vicinity of I85 is in this text file (right click the file and choose "open in new window" or "open in new tab" to open the file): BAdegrees. You can use statcrunch to plot this data on a Google map as follows:

  • Right click Google maps at statcrunch.com and choose "open in new window" or "open in new tab" to open the Google mapping facility at statcrunch.com.
  • Below the map in the Location information window copy and paste the location information from the above text file.
  • In the Legend title window type the word Counties.
  • In the Optional legend information window copy and paste the optional legend information from the above text file.
  • Click the Plot locations button below the Optional legend information window.
  • Your data will begin to plot on the Google map (the data will take a few seconds to appear since Google servers will process only one "geocode" request per second).
  • The map will have "baloon" markers showing the location of the counties. Point to a marker to see the name and proportion for that county; click on the marker to open a window with the information. Alternatively, click a county name in the list to the right of the map to see the location and information for that county.


Question 1. A major trucking company is located in Danville, Virginia. Simply by looking at the map, which county for which you have an estimated proportion is closest to Danville? (click-and-hold on the map and drag it down a little to see Danville, VA on the map).

    

A community college in Statesville, NC will offer technical training to Apricot employees at a reduced cost. The Apricot CEO would like a 95% confidence interval for p, the proportion of the population over the age of 25 with a bachelors degree, in the county closest to Statesville, NC.

Question 2. Calculate the confidence interval for the county closest to Statesville; assume the sample size n = 750.

lower bound (use 4 decimal places)
upper bound (use 4 decimal places).
 
 
 

A poll found that 64% of a random sample of 1076 adults said they believe in ghosts.

Question 1. Find the margin of error zsqrt(((p^^\^)((1-p^^\^)))/n), abbreviated ME, for this poll if we want 90% confidence in our estimate of the proportion of adults who believe in ghosts.
ME=

(Round to 3 decimal places.)

Question 2. Explain what this margin of error means.
    
Question 3. If we want to be 99% confident, will the margin of error be larger or smaller?
    

Question 4. Find the margin of error needed to be 99% confident.
ME= (Round to 3 decimal places.)

Question 5. In general, if the sample size and all other aspects remain the same, will smaller margins of error be associated with confidence intervals that have greater levels of confidence or lower levels of confidence? 1 submission only.
    
 

Subject General
Due By (Pacific Time) 10/26/2013 12:00 am
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