AP Statistics Final Project- Megan Lally and Ava Lewellyn

Stats Final Project

Megan Lally & Ava LewellynMr. Lombardozzi 2023

Research Question

DOes the data provide convincing evidence of the true proportion of MTS High School students who are depressed is greater than the 15% of high school students in Connecticut at the .05% significance level?

Why this research question...

• We were interested with the levels of mental health throughout Connecticut and in our own community.
• Due to our interests in mental health, we created our research question.
• People around the school filled out a survey we created in order to collect our data and analyze it compared to the research we found for Connecticut teen mental health.

Description of Sampling Procedure

We scored each chart individually for the people who answered 7-10 for the first question and more than half the days/very difficult or nearly every day/extremely difficult. These people were named in our results As depressed or having difficult Issues with mental health.

Chart 1

This chart is skewed left with more people not feeling sadness in the last two weeks (scored 7-10 for depression).

Chart2

This chart is skewed to the left with more people not feeling down or hopeless in the past 2 weeks. Only 12.8% of people would be in the category of depressed for this section.

Chart 3

This chart is skewed to the left because most people didn't have little interest or pleasure in doing things in the past 2 weeks. Only 15.9% of people felt little interest or pleasure in doing things in the past 2 weeks.

Chart 4

This chart was only slightly skewed to the left with the righ side having 34.2% of people feeling tired or having little energy in the past 2 weeks.

Chart 5

This chart is skewed to the left because only 17.1% of people felt bad about themselves, thought that they were a failiure, or let themself/their family down in the past 2 weeks.

Chart 6

This chart was skewed to the left with majority of people having no difficulties with the other mentioned problems affect their work, taking care of things at home, or getting along with other people in the past two weeks. These issues only affected 17.1% of people in our study.

Potential problems and improvements

Problems

• People could have lied and there would be nothing we could do about that because only the people answering the questions know their personal answer .

Improvements

• To improve, we could have a less bias approach because we asked people to do it instead of just having it randomly distributed.

VS

Conclusion

Calculations

With a P-value of .08 being grater than our significance level of .05, we fail to reject Ho. We do not have convincing evidence that the true proportion of MTS High School students that are depressed is greater than .15.

1-Prop Z Testprop < .15 z= -1.38620656 p= .082841974 p̂= .08 n=50

Final summary

To answer our original question of interest, the true proportion of MTS High School students who are depressed is NOT greater than the 15% of high school students in Connecticut. This shows that the data did not provide convincing evidence of more than 15% of students being depressed that we surveyed and picked randomly. We could improve on our study by having a whole school survey where people would be less likely to lie because people who take it have the choice to. This would allow us more data and we could eventually have a large sample to randomly take our data from. The limitations of the project was getting the data we needed since we needed to individually ask people to fill out our survey, as well as the research we had access to due to our topic being based around mental health and depression.

To better answer the question of interest, with a larger sample, we would be able to better accurately find a more presice percentage of MTS High School studdents who are depressed.

thankyou!