Statistics students survey GHS students

GULF HIGH SCHOOL, March 1, 2008.—Students in my AP Statistics class have conducted a study about Gulf High students, using random sampling.

The results depend on the fact that, according to statistical theory, a good approximation about the characteristics of a population (in this case all of the students at GHS) can be determined by surveying a relatively small number of people (in this case, a random sample of the students).

National polls rely on this principle. For example, the Gallup poll normally interviews only about 1500 Americans to predict the outcome of a national election.

My students created a random sample of 60 Gulf High students. One way we might have done this would be to have put the name of each GHS student on a piece of paper and put all of the papers in a large hat and randomly draw names. That would be somewhat impractical, so earlier this year a computer text file was created with the names of every student, taken from eSembler. The computer software numbered the students from 1 to 1714. A student repeatedly entered “RANDOM(1714)” on a TI-89 calculator, which returned a random number between 1 and 1714, thus picking the 60 students for us.

If we had used stratified random sampling, we might have picked a certain number of students from each grade and a certain number of male and female students. But the randomization process tends to ensure that an appropriate number of students in each grade will be selected.

Although we attempted to reach 60 students, as of this date 51 surveys have been returned. We know that at least two of the missing surveys were sent to students have withdrawn from school. The 51 returned surveys were as follows:

One of the questions asked was, “Do you have a myspace page?” The results were:

Boys: yes, 18; no, 5.
Girls: yes 24, no 4.

Thus, 82% of the students in our survey have a myspace page. Using statistics, we used the sample information to make an inference about the population, that is, the entire student body. Using a z-test, we concluded with 95% confidence that the true proportion of Gulf students who have a myspace page is between .719 and .928. In other words, the margin of error for the survey was plus-or-minus about 10%. We could have decreased the margin of error by increasing the sample size.

While it looks as if a higher percentage of girls than boys have myspace pages, we did not have large enough numbers to perform a chi-square test to make an inference about whether or not this is true.

Students were also asked, “Do you approve of the job George Bush is doing as President?” (This is a question that the Gallup poll has asked every year since 1935, with this exact wording.) The results were as follows:

Boys: approve, 3; disapprove, 13; not sure, 7
Girls: approve, 2; disapprove, 20; not sure, 6
Total: approve, 5; disapprove, 33, not sure, 13

Clearly, only a small proportion of Gulf students approve of the job President Bush is doing. In fact, we can conclude with 95% confidence that the actual percentage of GHS students who approve is between 1.6% and 18.0%. If we settle for 85% confidence, we conclude the actual percentage of GHS students who approve must be between 3.8% and 15.8%.

We were interested in what percentage of Gulf students smoke cigarettes. The actual question was, “Have you smoked a cigarette in the last seven days?” This is probably a question for which response bias might be an issue, meaning that the person being questioned might give an untrue answer. Further complicating this is the fact that the student's name was written on each survey; however, it was difficult to arrange a completely anonymous survey.

Of the 51 students who have returned the surveys, 3 boys and 3 girls stated that they had smoked within the last week.

About 14% of the respondents said they were left handed. This is in close agreement with the generally recognized proportion of persons who are left-handed.

We asked students what their favorite radio station was. The results:

         91.5  93.3  97.9  97X  95.7  99.5  98.7  None
Male      0      2    3     7    1     4     2     5
Female    2      5    2    10    4     0     4     2

      

We also asked students their favorite candidate for President. The survey was generally completed when all of these named candidates were still running.

        Obama Clinton Huckabee Romney McCain Other Kucinich Edwards Paul Giuliani Hunter
Male      6     3        2       1       6     1      0        2      1     1       0
Female   11     8        2       0       2     2      3        0      0     0       0

Some other questions on the survey have not yet been analyzed. This article may be updated when they are examined, or if any outstanding surveys are returned.