## Statistics Tutorial

#### Intro

Being able to draw conclusions based on statistics is a very important component to understanding your results. By viewing the research question, parameter(s) of interest, sample statistic, and p-value, we can conclude what the results of the research were. In this problem, you will be given the above information and it is up to you to write a coherent conclusion paragraph (with complete sentences) that summarizes the results of the research.

#### Sample Problem

Students often use excuses for why they were late to class. A common excuse is that the student’s car had a flat tire. If students are lying about the flat tire, they may pick a certain tire disproportionately.
So the question is: do students pick which tire went flat in equal proportions? It has been conjectured that when students are asked this question and forced to give an answer (left front [LF], left rear [LR], right front [RF], or right rear [RR]) off the top of their head, they tend to answer “right front” more than would be expected by random chance.
To test this conjecture about the right front tire, a recent class of 28 students was asked if they were in this situation, which tire would they say had gone flat. We obtained the following results:
LF: 6; LR: 4; RF:14; RR: 4
The parameter of interest (pi) is the long-run probability that students choose the RF tire. Null hypothesis: pi = 0.25. Alternative hypothesis: pi > 0.25.
Sample statistic: p-hat = 14 students choosing RF / 28 total students = 0.50.
Using a one-proportion t-test, we get a p-value of 0.001 and a z-score of 3.07.

Formulate a conclusion, incorporating relevant information from the above problem. Can we generalize these results to the general population?

#### Solution

Based on this study, we conclude that we have strong evidence against the null hypothesis and we will reject it; we have strong support for the alternative hypothesis as well. The low p-value (< 0.01) and high standardized statistic (> 3.0) suggest that 50% of the students choosing the right front tire by simply guessing from the four tires is extremely unlikely. We therefore also conclude that random chance does not play a factor in students’ choice of tire in this scenario. So, students do not pick which tire went flat in equal proportions but they instead are more likely to choose the right front tire.

We cannot generalize a study of this case to the general population. The scope of this study focuses on a small class of only 28 students. Furthermore, these students could all be from very similar backgrounds or parts of the country and are most likely in a similar age range. We could, however, potentially generalize to students at the school in general, though we cannot be certain without more information about the class and the school population. We would need to know how representative this class is of the school population. Ultimately, because we cannot exclude extraneous variables (such as age, background, etc.), we cannot generalize such a result to the general population due to the low likelihood that the sample is representative of the general population. 