HW1 Solutions

The assignment:

Do Problems 1.2, 1.7, 1.8, 1.12 (except parts b and g) and 1.13 (a,c and d).

Referring to the Cato Report Lies, Damned Lies and 400,000 Smoking Related Deaths answer the following questions:

1. What do you think the target population of the American Cancer Society's Cancer Prevention Survey (CPS) was?
2. How did the sampled population differ from the target population?
3. What was the result of the non-representative sample on the CDC estimate of "cancer related deaths"?
4. Who had a higher mortality rate (number of deaths per thousand people): smokers who participated in the CPS or all Americans combined?

Solutions:

(59 points total)

Problem 1.2 (5 points)

Descriptive statistics confines itself to the dataset at hand. Inferential statistics includes making generalizations from a sample to a population.

Problem 1.7 (5 points)

A sample is a group of subjects that are actually observed. A population is a larger group of subjects about which we want to make inferences. The sample is a subset of the population.

Problem 1.8 (5 points)

A representative sample has characteristics typical of the target population. It is not possible to accurately generalize from a sample to a population if that sample is not representative.

Problem 1.12 (3 points each, 15 points total)

a) All students enrolled your section of STAT 110

c) Census since all members of the population are included in the sample.

d) Sample since only some members of the class are included in the sample

e) 100% reliability since we would know the population mean without error

f) An estimate based on 10 students very probably not be the same as the population mean. Reliability would increase with sample size if the sample is randomly selected.

Problem 1.13 (3 points each, 9 points total)

a) The target population appears to be all adult individuals in the US. The sampled population are all individuals (or adults in the continental US) who own phones and are at home during the hours when the poll was conducted.

c) The sample is the 2,000 people contacted

d) The inference is an estimate of the percent of Americans that hold a specified opinion.

Referring to the Cato Report Lies, Damned Lies and 400,000 Smoking Related Deaths answer the following questions:

1. (5 points) What do you think the target population of the American Cancer Society's Cancer Prevention Survey (CPS) was?
   
   All American adults
    
2. (5 points) How did the sampled population differ from the target population?
   
   The sampled population was more affluent and tended to be white, college graduates and tended not to have hazardous jobs compared to the target population.
    
3. (5 points) What was the result of the non-representative sample on the CDC estimate of "cancer related deaths"?
   
   The fact that the sampled population had lower death rates than the target population caused the estimates of "cancer related deaths" to be exaggerated.
    
4. (5 points) Who had a higher mortality rate (number of deaths per thousand people): smokers who participated in the CPS or all Americans combined?
   
   Americans in general had higher mortality rates than smokers in the CPS.

E-mail Mr. Callahan at stat110@edcallahan.com with questions or comments about this web site or about the class itself.