AP Stats Final Project

Question?

• Is there evidence at the .05 level that music students get higher mean ACT scores than students who don’t participate in music?

• Test chosen – Two sample T-test

Hypothesis

• H₀: μd = 0 – Music students have the same mean ACT scores as regular students.

• Hₐ: μd > 0 – Music students have a higher mean ACT score than students not in music.

The 5 W’s

• Who – students who participate in music and those who don’t

• What – mean ACT scores • When – now• Where – Lincoln Southwest High-school• Why – to determine whether or not music

students have higher mean ACT scores than other students

Experimental Design

• We designed a survey that had more than just ACT scores as to not make it obvious as to what was being tested. We then randomly selected 3 of the classes Holly and I are in to survey. Other school activities were listed on the sheet such as athletics and speech as to not draw attention just to music. The data was then sorted into music and non-music students.

Assumptions and Conditions

• Random – classrooms surveyed were selected randomly

• 10% condition – those surveyed represent less than 10% of southwest (49 students)

• Independence – each student’s ACT score was independent of the other students

• Nearly normal – graph on next page • Group Independence – music students don’t affect

the scores of those not in music

Music Students Non-music Students0

1

2

3

4

5

6

Graphed data

Freq

uenc

y of

ACT

Sco

res

Nearly Normal Proof

Running the Test

Screen Dump InputDataList1: L1List2: L2Freq1: 1Freq2: 1μ 1> μ2Pooled: No

Outputμ1 > μ2t=4.623034p=0.00002058df=37.363613

Conclusions

• Reject null hypothesis with a p-value of ~0.• Given there is no difference in the mean ACT

scores of music students and non-music students there is a 0% chance that music students would score higher like this due to natural variation.

• Answer to original question: Yes, music students have higher mean ACT scores.

Additional Summary Statistics

• L1: Music• L2: Non-music• Sx1=3.06• Sx2=3.56• N1=17• N2=32