INTRO:
This assignment has to do with polls and surveys. This is perhaps one of the most common applications of statistics. Surveys and polls are done in economics, business, health, social sciences, education, etc. Sciences such as biology also use these methods although usually in a different context. (What percentage of deer survived the winter?)

All of these questions involve proportions , which is a statistical term for percentages. You will need the following topics from the book to answer the questions:

Confidence interval for one proportion

Confidence interval for difference of two proportions

Sample size for proportions

Hypothesis Test, one proportion

Hypothesis Test, independent samples, difference of two proportions

Here is the link for the Alaskan portion of a recent US Census Bureau survey:

http://www.census.gov/acs/www/Products/Profiles/Chg/2003/ACS/AK.htm

Have a look around. There is a lot there, and maybe you will find material for your own project.

I downloaded data from Table 3, "Economic Characteristics". For interest take a look at the original spreadsheet. This entire assignment has to do with the unemployment rates. Obviously there is way more here than this. You could feel free to do your project from this survey if you like.

Proportions can be presented as a percentage, ie 5%, or as a relative frequency, ie 0.05.

1. 5 points
   First before a survey is done, it is wise to compute sample size requirements.
   This sort of thing is discussed in chap. 8. Find the sample size formula for proportions. Suppose we wish to estimate the unemployment rate in Alaska. Eventually we will be computing a 95% confidence interval for the unemployment rate. When we go on TV, and announce the unemployment rate, we would like to be less than 1.5% from the true unemployment rate. What sample size would be required to accomplish this?
2. 5 points
   The survey estimates the Alaska unemployment rate as 10.8% in 2003, and 7.8% in 2000.
   (The word RATE, is yet another way to refer to a proportion.) These percentages are called "point estimates" of the unemployment rate. With the 2000 and 2003 sample sizes below, compute the margin of error, E, for both point estimates.
   
   Year Interviews
   2003 4015
   2002 3496
   2001 4000
   2000 3607
   Confidence intervals for proportions require that np, and nq both be larger than 5.
   For 2003, check if both np > 5 and nq > 5?
3. 5 points
   There are two competitive ways to present these confidence intervals.
   Method 1
   point estimate margin of error
   The margin of error is the quantity E.
   Method 2
   Or alternatively... (lower limit , upper limit)
   The upper limit is the point estimate + margin of error.
   The lower limit is the point estimate - margin of error.
   Depending on the field, one or both of these methods may be in common use.
   Find confidence intervals for the unemployment rates in 2000 and 2003. Then present both intervals by both methods. A confidence interval is called an "interval estimate".
   METHOD 1

   Year	Unemployment rate
   2000
   2003

   
   METHOD 2

   Year	Unemployment rate
   2000
   2003

   
   A plot for confidence intervals
   Confidence intervals can be graphed in a variety of ways. If it so happens that you have multiple confidence intervals for your semester project or for your doctoral thesis you might try to present them like this. It shows in a clear visual way the trend in unemployment. The 2003 and 2000 confidence intervals do not overlap. This gives us an indication about the result of the up coming hypothesis test. This graph can be done with the HI-LO option under the financial types of graphs in Excel. This is described in the power point lecture on graphing techniques.
   
   

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4. 5 points
   Compute a confidence interval for the difference in employment rates from 2000 to 2003.
   See chapter 8, on comparing two proportions. (Present it in your preferred method from above.)

   Difference in Unemployment rate 2000-2003

   (-0.0427, -0.0173)

   
   Does the interval contain zero? YES or NO? _______ _____
   What inference can you make about the employment rates in 2000 and 2003?
5. 5 points
   Chap 9 gives Hypothesis Testing for a difference in two proportions
   Conduct a hypothesis test to see if the unemployment rate in 2003 is significantly more than the employment rate in 2000.
   Ho: p ₂₀₀₃ = p ₂₀₀₀
   Ha: p ₂₀₀₃ > p ₂₀₀₀
   What is the formula (no numbers) for the test statistic?
   Compute the test statistic. What is the p-value of the test statistic?
6. 10 points

Identify any proportion(s) that's interesting to you. Describe the quantity in words so I know what you are looking at:

Price: $26.39

Solution: The downloadable solution consists of 15 pages, 1139 words and 13 charts.
Deliverable: Word Document