1 of 13

Are more male seniors going on to major in math or science than female seniors in the year of 2014 at Pioneer High School?

By: Anisha Shah & Mia Bajic

Mrs. Campiotti

Period 5

2 of 13

We set out to answer the question: Are more male seniors going on to major in math or science than female seniors in the year of 2014? An affirmative conclusion would be compelling evidence in arguing that there is a gender gap and that female students need more exposure to STEM programs. A negative conclusion would indicate insignificant evidence.

In other words...

Is there a statistically significant difference in the proportion of male seniors going on to major in math or science and the proportion of female seniors going on to major in math or science?

We determined to use a two-sample z-test for a difference in proportions (pm-pf)

Ho: pm-pf=0

Ha: pm-pf>0

Where pm is the proportion of male seniors going on to major in math or science
Where pf is the proportion of female seniors going on to major in math or science

Intro: The Question

3 of 13

Methodology

First, we assembled two lists of class periods for regular senior English and AP English Language to prevent undercoverage because every senior takes an English class. We blocked by class type to make sure our samples included all types of students and that differences could not be the result of this possibly confounding variable. The morning of the sampling, we gave Mrs. Andrade, Mrs. Fahrner, and Ms. Clem each as many slips of paper as they have students in each period of theirs from which we are sampling. Each student answered the slips anonymously and independently.

For regular English, we assigned each teacher-period combination a number 1-7. Using a random number generator (1-7), we selected two numbers, ignoring repeats. We got 7 and 5, and chose the corresponding teacher-period combination, which was Mrs. Fahrner’s first period and Mrs. Andrade’s second period. These are the periods we used for regular senior English (ERWC).

For the AP English Literature list, we assigned each of Ms. Clem’s periods a number 1-4. Using a random number generator (1-4), we selected two numbers, ignoring repeats. We got 2 and 3; we picked according periods which were 3rd and 4th period.

4 of 13

Example Survey

Circle Your Gender: Male or Female Are you going to college? Yes or No If yes, circle your intended major: Math \| Science \| Humanities \| Social Science \| Engineering \| Other \| Undecided

5 of 13

Data Collection Table

Regular English	AP English Literature
1. Ms. Montelibano’s 4th period	1-Ms. Clem’s 2nd period
2. Ms. Montelibano’s 5th period	2-Ms. Clem’s 3rd period
3. Mr. Goldman-Hall’s 5th period	3-Ms. Clem’s 4th period
4. Mr. Goldman-Hall’s 6th period	4-Ms. Clem’s 5th period
5. Ms. Andrade’s 2nd period
6. Mrs. Andrade’s 3rd period
7. Ms. Fahrner’s 1st period

*Bold indicates classes that were chosen*

6 of 13

Analysis

Two-sample Z-test for a difference in proportions (pm - pf)

This inference procedure is appropriate because we are estimating the difference between two population proportions.

Conditions:

Random? The data came from randomly selected English classes. Therefore, the random condition is satisfied.

Normal? nmp̂m ≥ 10 → (42)(0.381) = 16 → 16 ≥ 10

nm(1-p̂m) ≥ 10 → (42)(1-0.381) = 26 ≥ 10

nfp̂f ≥ 10 → (54)(0.241) = 13 ≥ 10

nf(1-p̂f) ≥ 10 → (54)(1-0.241) = 41 ≥ 10 All successes and failures are above ten, so the Normal condition is satisfied.

Independence? 120(10)= 1200 → It is safe to assume that there are at least 1200 seniors in California public high schools. Ergo, the sample size of 120 students is no more than 10% or of seniors in California public high schools with similar demographics, and the independent condition is met.

7 of 13

Analysis continued

α = 0.1

P(z > 1.475) = 1 - P(z < 1.475) = 0.07

(0.381-0.241) - 0

(0.381)(1-0.381) + (0.241)(1-.0241)

42 54

p-value = 0.07

8 of 13

Regular English

9 of 13

AP English Literature

10 of 13

Both classes combined

DESCRIPTION

12 of 13

Interpretation

Since the p-value 0.07 is less than alpha (0.1), the sample result is statistically significant at the 10% significance level. We have sufficient evidence to reject Ho, and conclude that the proportion of male seniors going on to major in math or science is greater than the proportion of female seniors going on to major in math or science. In other words, we conclude that there are more male seniors going on to major in math or science than female seniors going on to major in math or science in the year 2014 at Pioneer High School.

Our results indicate that if this study were repeated many times with a variety of samples from different public schools in California, and the results were still statistically significant, these data could prove to be compelling evidence in arguing that there is a gender gap in math and/or science majors. This could be used to argue for STEM programs that support female students interested in these majors.

13 of 13

Improvements

Since five people put question marks next to the Gender question, we could make an Other option for gender if we were to repeat this study, so that there would be no response bias in any of the questions. However, this change would not help make our results more accurate.
Four people were absent in one of the regular English classes, resulting in nonresponse bias, so we could try to make sure that didn’t happen if we repeated it, but it is impossible to predict absences.
If we had had more time, we could have randomly selected more classes from which to sample, so as to increase the accuracy of our results.
In addition to English classes, we could have included all Government classes since that is a required subject for seniors as well. This would be one way of increasing our sample size, ignoring repeats.