1. A marketing research company has a contract to estimate the percentage of people listening to radio talk shows in several U.S. cities. They are using a sample size of 1,000 in Amarillo, Texas which has about 250,000 residents. The company is very satisfied with the accuracy of their estimates for Amarillo using this sample size of 1,000.

Dallas, Texas has about four times the population of Amarillo, but very similar demographics (i.e. similar gender, age, racial, and economic distributions for example). To get approximately the same accuracy in their estimates for Dallas as in Amarillo what should the sample size be? (5 points)
  1. 1,000
  2. 2,000
  3. 4,000
  4. 16,000
  5. None of the above

 

  1. Should the United Nations continue to have its headquarters in the United States? A television program asked its viewers to call in with their answers for that question. There were 184,900 callers and 67% said "NO".

A newspaper conducted a survey by interviewing a nationwide random sample of 900 adults and found that 72% answered "YES" to the exact same question (i.e. same wording).

Which statistic do you believe to be a more reliable estimate of American opinion on this issue and why? (10 points, be brief, calculations are not required for a correct answer, but if they help you, go ahead)

 

 

 

 

 

 

3. A poll reported in Time magazine (February 1995) asked 361 adult Americans the question "Do you think Congress should maintain last year's ban on several types of assault weapons?" 75% responded "yes".
    1. What is the standard error for the sample percentage (5 points), show your work and calculate a number:

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    2. Using the information reported in the Time magazine results above, construct an approximate 95% confidence interval for the population proportion, p. If it is not possible to do this, please write "not possible" on your answer sheet and explain your reasoning here. (5 points)

 

 

 

 

 

 

 

 

 

 

4. M & Ms, a type of candy, are manufactured in the following proportions:

Color

Red

Yellow

Brown

Green

Blue

Orange

Proportion

.2

.2

.3

.1

.1

.1

Suppose we play a game. I have an infinitely large bag of M & Ms and I allow you to close your eyes and reach in and select 100 at random (treat it as if it were a random sample of 100). You win $9 for each blue one you select and you lose $5 for each brown one you select. You neither win nor lose money for picking M & Ms of the other colors. You cannot choose not to play.
    1. Calculate the expected value (5 points) and standard error (10 points) of the total "winnings" for a sample of 100 M & Ms from this bag.

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    2. You lost $158 to me after picking 100 M&Ms at random from the bag. What was your chance of losing $158 or more to me? (5 points)

 

 

 

 

 

 

 

 

 

5. Suppose it is known that 10% of all Americans believe that the world will end at midnight on January 1, 2000. A magazine would like to know exactly why this 10% believes the world will end, so a nationwide simple random sample of 121 is selected for in-depth interviews. What is the chance that between 5% and 9% of the sample of 121 will believe the world will end? (10 points)