The study

by dena raheem & tia elkhatib

The sample that Tia and I used was a random sample that consisted of 50 teachers from NOHS. I found a roster of every staff member at the high school which had the names of every teacher in the building as well as every principal and guidance counselor. The population of interest therefore was the teachers, guidance counselors, and principles at North Olmsted High (all the people listed on the roster). The roster itself consisted of about 117 names on it. I typed up every name of every person on the sheet and cut up the names into individual strips of paper. I then took each of the strips and put them into an envelope. I randomly pulled out 25 names, shaking the envelope between every name I pulled out. I then handed the envelope to Tia where she did the same exact. She pulled out 25 names on top of the 25 names I randomly drew. Those strips of names we pulled out were what we used as the sample.

Our method of obtaining our results from the sample was not a survey. We instead thought it would be more reliable ourselves to actually ask the teachers themselves. So during first period, AP Statistics, Tia and I wandered the halls to track down the teachers we needed. We even looked up where some teachers were located first period in order for us to ask them. We asked each of the 50 teachers the same question, "Where doing a study for Stats, and we just want to know your favorite color". The question was as simple as that. Out of the fifty people that were in the survey, 47 of them responded. Two of them were not able to be reached and one of them claimed, " I don't wanna participate"- a real jerk of a teacher said that...

More information about our data
raw data | graphs

chi-squared test results

by dena and tia

Null Hypothesis: There is not an association with teachers of different subjects and their favorite colors.

Alternative Hypothesis: The is an association among teachers of different subjects and their favorite colors.

α= .05

Test Statistic:

Assumptions: An independent, random samples, and cell counts of 5 or more (which is not the case here).

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Tabulated statistics: subject, color

Rows: subject Columns: color

black blue green purple red yellow All

art 0 1 1 1 1 0 4
0.1702 1.5319 0.5957 0.5957 0.7660 0.3404 4.0000

business 0 3 1 0 1 0 5
0.2128 1.9149 0.7447 0.7447 0.9574 0.4255 5.0000

english 0 4 1 1 1 1 8
0.3404 3.0638 1.1915 1.1915 1.5319 0.6809 8.0000

esl 0 0 0 0 2 0 2
0.0851 0.7660 0.2979 0.2979 0.3830 0.1702 2.0000

foreign language 1 1 0 0 1 2 5
0.2128 1.9149 0.7447 0.7447 0.9574 0.4255 5.0000

math 0 3 1 0 1 0 5
0.2128 1.9149 0.7447 0.7447 0.9574 0.4255 5.0000

phys. ed 0 0 0 0 1 0 1
0.0426 0.3830 0.1489 0.1489 0.1915 0.0851 1.0000

science 0 1 1 1 1 0 4
0.1702 1.5319 0.5957 0.5957 0.7660 0.3404 4.0000

social studies 1 5 1 2 0 0 9
0.3830 3.4468 1.3404 1.3404 1.7234 0.7660 9.0000

special ed. 0 0 1 2 0 1 4
0.1702 1.5319 0.5957 0.5957 0.7660 0.3404 4.0000

All 2 18 7 7 9 4 47
2.0000 18.0000 7.0000 7.0000 9.0000 4.0000 47.0000

Cell Contents: Count
Expected count

Pearson Chi-Square = 43.086, DF = 45
Likelihood Ratio Chi-Square = 44.273, DF = 45

* WARNING * 46 cells with expected counts less than 1
* WARNING * Chi-Square approximation probably invalid

* NOTE * 60 cells with expected counts less than 5

Tabulated statistics: subject, color

Rows: subject Columns: color

black blue green purple red yellow All

art 0 1 1 1 1 0 4
0.170 1.532 0.596 0.596 0.766 0.340 4.000

business 0 3 1 1 1 0 6
0.255 2.298 0.894 0.894 1.149 0.511 6.000

language 1 5 1 1 4 3 15
0.638 5.745 2.234 2.234 2.872 1.277 15.000

math 0 3 2 0 1 0 6
0.255 2.298 0.894 0.894 1.149 0.511 6.000

science 0 1 1 2 2 0 6
0.255 2.298 0.894 0.894 1.149 0.511 6.000

social studies 1 5 1 2 0 1 10
0.426 3.830 1.489 1.489 1.915 0.851 10.000

All 2 18 7 7 9 4 47
2.000 18.000 7.000 7.000 9.000 4.000 47.000

Cell Contents: Count
Expected count

Pearson Chi-Square = 16.960, DF = 25
Likelihood Ratio Chi-Square = 21.220, DF = 25

* WARNING * 20 cells with expected counts less than 1
* WARNING * Chi-Square approximation probably invalid

* NOTE * 35 cells with expected counts less than 5

Tabulated statistics: subject, color

Rows: subject Columns: color

black blue green purple red yellow All

analytical 0 7 4 3 4 0 18
0.766 6.894 2.681 2.681 3.447 1.532 18.000

creative 2 11 3 4 5 4 29
1.234 11.106 4.319 4.319 5.553 2.468 29.000

All 2 18 7 7 9 4 47
2.000 18.000 7.000 7.000 9.000 4.000 47.000

Cell Contents: Count
Expected count

Pearson Chi-Square = 4.984, DF = 5
Likelihood Ratio Chi-Square = 7.014, DF = 5

* WARNING * 1 cells with expected counts less than 1
* WARNING * Chi-Square approximation probably invalid

* NOTE * 9 cells with expected counts less than 5

Tabulated statistics: subject, warm/cool

Rows: subject Columns: warm/cool

cool neutral warm All

analytical 14 0 4 18
12.255 0.766 4.979 18.000

creative 18 2 9 29
19.745 1.234 8.021 29.000

All 32 2 13 47
32.000 2.000 13.000 47.000

Cell Contents: Count
Expected count

Pearson Chi-Square = 1.956, DF = 2
Likelihood Ratio Chi-Square = 2.649, DF = 2

* WARNING * 1 cells with expected counts less than 1
* WARNING * Chi-Square approximation probably invalid

* NOTE * 3 cells with expected counts less than 5

Tabulated statistics: subject, warm/cool

Rows: subject Columns: warm/cool

cool warm All

analytical 14 4 18
13.02 4.98 18.00

creative 20 9 29
20.98 8.02 29.00

All 34 13 47
34.00 13.00 47.00

Cell Contents: Count
Expected count

Pearson Chi-Square = 0.431, DF = 1, P-Value = 0.511

* NOTE * 1 cells with expected counts less than 5

P-value = .511 Degrees of Freedom = 1
-fail to reject the null hypothesis