Is the proportion of high school seniors at Tates Creek who skip frequently greater than that of all high school seniors in the 6^th district?

By Jordan Brown and Nick Collar B2

Disclaimer: This study was done in an AP Statistics course with relatively small sample sizes. The validity of such studies must always be questioned. Please keep this in mind if you use or report the results of this study.

Abstract:

High School Seniors across the country have a habit of skipping school frequently. The goal for this study was to determine if the proportion of seniors who skip school frequently (5 or more times in a school year) at Tates Creek is greater than the proportion of seniors who skip frequently in the 6^th District high schools of Kentucky. The outcome that was expected is that Tates Creek has a greater proportion of seniors who skip frequently. This hypothesis was determined by observing a large number of seniors at Tates Creek who skipped frequently.

The population from which inferences will be drawn is all seniors at Tates Creek High School. A sample size of 40 randomly selected seniors was used. Using a one-proportion z-test, the sample data was compared to the proportion of seniors who skip frequently in the 6^th district high schools. The sample data showed that the proportion of seniors who skip frequently is 0.5. Te null hypothesis in the z-test is the claim that the proportion of seniors at TC who skip frequently is the same as the proportion of seniors in the 6^th district. It was tested against an alternative hypothesis (Ha), which is that the proportion of seniors at TC who skip frequently is greater than that of seniors in the 6^th district.

Methodology:

To answer the question of whether or not the proportion of seniors at TC who skip frequently is greater than the proportion of seniors in the district, the proportions of each must be found. In order to find the proportion at Tates Creek, each of the 337senior students at TC were assigned a number. (001-337) Using a random number generator, a sample size of n=40 was obtained. Each of the students names were given to the attendance clerk at Tates Creek High School. The clerk then gave the numbers of how many skips each student in the sample had for the 2003-2004 school year. The names of each student were kept confidential for legal purposes and only the numbers of skips were given. In order to find the proportion of seniors who skip frequently in the 6^th district, we contacted pupil personnel at the administration office of the 6^th district school system. This information was used in our one-proportion z-test to determine if the proportion of seniors who skip often at Tates Creek is significantly greater than the district average.

Analysis and Inference:

The first step we took in drawing inference from our data was to check the assumptions of a one-proportion z-test. We know that our data was obtained randomly and is an SRS. We needed to find the proportions for Tates Creek and for the 6^th district. 20 of the 40 students in our SRS of Tates Creek seniors had 5 or more skips in the 2003-2004 school year. So po is equal to 0.5. (observed # of successes divided by the total # of subjects) The proportion of seniors who skip in the 6^th district is 0.46 according to pupil personnel in the 6^th district high schools. Two more assumptions that need to be met are n(po)>10 and n(1-po)>10 in order to draw inference from our significance test.

40(.5)>10 and 40(1-.5)>10

Our assumptions are met. Next, we set up our null and alternative hypothesis. As we mentioned earlier, the null is the claim that the proportions are the same, and the alternative is the claim that the proportion of seniors who skip frequently is greater than the district proportion.

Ho: p=.5

Ha: p<.5

(p is the proportion of seniors in the district who skip frequently)

Our critical z score was found algebraically and through the use of a graphing calculator.

Z= .5-.46 = .5076

By using a z table and using a graphing calculator, we were given a p-value of P=.6941. This p-value is the probability of a result being different than the one we obtained. Therefore, the smaller the p-value is, the stronger evidence there is against the null hypothesis. P=.6941 is very large though!

We cannot call our data statistically significant at an =.05 level. This is because 0.6941>0.05.

Because our data is not statistically significant at an =.05 significance level, we fail to reject the null hypothesis. This means that there is not significant evidence to support the claim that the proportion of seniors at Tates Creek who skip frequently is greater than the proportion of all seniors in the 6^th district high schools. Although the sample proportion we obtained is larger than the district proportion, sampling variability could have accounted for this increase. We would need to take much larger sample sizes and replicate the test many times in order to get more accurate results to draw inference from.