Mathematics
statistical concepts

### Question Description

Focus of the Final Exam

The purpose of the Final Exam is to assess your understanding of the main statistical concepts covered in this course and to evaluate your ability to critically review a quantitative research article. The exam will consist of two parts: Part I includes three essay questions and Part II includes a research critique. All of your responses should be included in a single Word document for submission.

Please include the following general headings for each section of the written exam within your Word document:
Part I: Essay Questions

1. Essay 1
2. Essay 2
3. Essay 3

Part II: Research Study Critique

1. Introduction
2. Methods
3. Results
4. Discussion

Your complete Word document must include a title page with the following:

1. Student’s name
2. Course name and number
3. Instructor’s name
4. Date submitted

Part I: Essay Questions
There are three essay questions in this section. You must answer all three questions. The length of each essay should be at least two double-spaced pages (excluding title and reference pages). Use 12-point font and format your paper with regular 1-inch margins. Do not include the essay prompt in your document. It will not count toward the length requirement for your essays.

Essay 1
A group of researchers conducted an experiment to determine which vaccine is more effective for preventing getting the flu. They tested two different types of vaccines: a shot and a nasal spray. To test the effectiveness, 1000 participants were randomly selected with 500 people getting the shot and 500 the nasal spray. Of the 500 people were treated with the shot, 80 developed the flu and 420 did not. Of the people who were treated with the nasal spray, 120 people developed the flu and 380 did not. The level of significance was set at .05. The proportion of people who were treated with the shot who developed the flu = .16, and the proportion of the people who were treated with the nasal spray was .24. The calculated p value = .0008.

For this essay, describe the statistical approaches (e.g., identify the hypotheses and research methods) used in this excerpt from a research study. Interpret the statistical results and examine the limitations of the statistical methods. Finally, evaluate the research study as a whole and apply what you have learned about hypothesis testing and inferential statistics by discussing how you might conduct a follow-up study.

• Describe the research question for this experiment.
• What were the null and alternative hypotheses?
• Were the results of this test statistically significant?
• If so, why were they significant?
• Would the researchers reject or fail to reject the null hypothesis?
• Do the results provide sufficient evidence to support the alternative hypothesis?
• What are some possible limitations to this study?
• Describe the difference between practical and statistical significance.

Essay 2
A researcher has investigated the relationship between IQ and grade point average (GPA) and found the correlation to be .75.

For this essay, critique the results and interpretation of a correlational study.

• Evaluate the correlational result and identify the strength of the correlation.
• Examine the assumptions and limitations of the possible connection between the researcher’s chosen variables.
• Identify and describe other statistical tests that could be used to study this relationship.

• How strong is this correlation?
• Is this a positive or negative correlation?
• What does this correlation mean?
• Does this correlation imply that individuals with high Intelligence Quotients (IQ) have high Grade Point Averages (GPA)?
• Does this correlation provide evidence that high IQ causes GPA to go higher?
• What other variables might be influencing this relationship?
• What is the connection between correlation and causation?
• What are some of the factors that affect the size of this correlation?
• Is correlation a good test for predicting GPA?
• If not, what statistical tests should a researcher use, and why?

Essay 3
A researcher has recorded the reaction times of 20 individuals on a memory assessment. The following table indicates the individual times:

 2.2 4.7 7.3 4.1 9.5 15.2 4.3 9.5 2.7 3.1 9.2 2.9 8.2 7.6 3.5 2.5 9.3 4.8 8.5 8.1

In this essay, demonstrate your ability to organize data into meaningful sets, calculate basic descriptive statistics, interpret the results, and evaluate the effects of outliers and changes in the variables. You may use Excel, one of the many free online descriptive statistics calculators, or calculate the values by hand and/or with a calculator.

Next, separate the data into two groups of 10; one group will be the lower reaction times, and the second group will be the higher reaction times. Then, address the following points in your essay response:

• Calculate the sum, mean, mode, median, standard deviation, range, skew, and kurtosis for each group.
• How do the two groups differ?
• Are there any outliers in either data group?
• What effect does an outlier have on a sample?

Lastly, double each sample by repeating the same 10 data points in each group. You will have a total of 20 data points for each group. After completing this, address the following in your essay response:

• Calculate the following for the new data groups: sum, mean, mode, median, standard deviation, range, skew, and kurtosis.
• Did any of the values change?
• How does sample size affect those values?

Part B: Research Study Critique
In this second portion of the Final Exam, you will identify and critically evaluate a quantitative research article based on a social science topic. Your selected article must include a research question(s) and/or hypothesis(es) and utilize statistical analyses covered in the course. The article must be peer-reviewed and published within the last 10 years.

In the body of your critique, describe the statistical approaches used, the variables included, the hypothesis(es) proposed, and the interpretation of the results. In your conclusion, suggest other statistical approaches that could have been used and, if appropriate, suggest alternative interpretations of the results. This process will allow you to apply the concepts learned throughout the course in the interpretation of actual scientific research. Your critique must include the following sections:

1. Introduction: This section will include a general introduction of the quantitative study from a peer-reviewed source published within the last 10 years. The research questions and/or hypothesis(es) as well as the purpose of the study should be clearly defined.
2. Methods: Describe and evaluate the procedures and methods of data collection, measures/instruments used, the participants and how they were selected, and the statistical techniques used.
3. Results: In this section describe and critique the results presented in the study.
4. Discussion: Discuss and evaluate the efficacy of the results presented in the study. Address, the strengths, weaknesses, and limitations of the study, and suggest future research directions. Include additional forms of statistical analyses as part of the suggestions for future research.

The Research Study Critique:

1. Must be at least four double-spaced pages in length (excluding title and reference pages) and formatted according to APA style as outlined in the Ashford Writing Center. Use 12-point font, with 1-inch margins.
2. Must use the sections and headings described above.
3. Must address the article with critical thought by examining, reflecting, and evaluating the article from an objective viewpoint and by using facts to support your argument. Refer to the Critical Thinking Community (Links to an external site.)Links to an external site. website for further assistance.
4. Must end with a conclusion that summarizes your critical evaluation.
5. Must use one quantitative research study from a peer-reviewed source that was published within the last 10 years.
6. Must properly cite the source article in APA style as outlined in the Ashford Writing Center.
7. Must include a separate reference page, formatted according to APA style as outlined in the Ashford Writing Center.

Carefully review the Grading Rubric (Links to an external site.)Links to an external site. for the criteria that will be used to evaluate your assignment.

Let me know if you have any questions!

1

Statistics Final Exam Essays
Statistics for the Behavioral Sciences
Dr. Jackson
Month Day, Year

STATISTICS FINAL EXAM ESSAYS

2

Part I: Essay Questions
Essay 1
The goal of this study was to compare the effectiveness of two types of vaccine: the flu
shot and the nasal spray. The null hypothesis was that the two types of vaccine were equally
effective. In other words, the proportions of individuals who developed the flu were the same for
the two samples. The alternative hypothesis was that the the two types of vaccine were not
equally effective. In other words, the proportions of individuals who developed the flu differed
for the two samples. The results of this test were significant, since the p-value was 0.0008. This
was below the significance level of 0.05. Thus, the researchers rejected the null hypothesis. The
results provided enough evidence to support the alternative hypothesis.
Both test conditions used large samples, with n=500 for each group. The participants
were randomly selected, though the exact selection procedure is not known. However, we
assume that, due to the large sample sizes, each of the samples contained at least 10 “successes”
and 10 “failures”. Also, despite the large sample sizes, the general population of individuals who
may potentially contract flu and be in need of the vaccine is many (more than 20) times larger
than each of the samples. We also assume the samples were independent, since a randomization
procedure was used.
Limitations of this study include the fact that the samples may not be representative of
the entire population of interest. Although a random sample was obtained, it may have been a
random sample of the local population, where certain demographic and health factors differ from
those nationwide or worldwide. For example, individuals in rural areas may be healthier than
those residing in major cities, and may have a higher natural resistance to flu. Such a difference
would affect the experimental results. Similarly, it is not guaranteed that the specific conditions

STATISTICS FINAL EXAM ESSAYS

3

of administering the vaccine were the same as they would be in all other circumstances. For
example, if this study was conducted during the summer, the effects may not be the same as what
they would have been during other seasons. Many other details that may affect the
generalizability of findings are absent from the study description. For instance, we do not know
for how long the patients were monitored after receiving the vaccine, while, in reality, the length
of time for a vaccine's effectiveness is very important.
A possible follow-up study could involve the effects of the vaccines for various age
groups, such as children, adults, and seniors. At the same time, we could assess the presence of
side effects for each demographic group, and for each vaccine type general. These findings
would be important in the practical applications of the vaccine, as patients will only be willing to
use it in the case it does not cause serious discomfort. It would also be helpful to compare each
of the vaccines to the baseline (the non-vaccinated) public, in order to check whether each
method produces a significant reduction in flu cases, as compared to the non-vaccinated
population.
The results of this study were statistically significant. However, statistical significance
differs from practical significance. Also, large samples tend to produce statistically significant
results, since a large sample size reduces the standard error. Sometimes, this results in a
phenomenon called the p-value fallacy, where a small p-value does not reflect meaningful
experimental conclusions or practical significance (Dixon, 2003). Any results that produce a pvalue smaller than the given alpha level will be statistically significant. However, in order to be
practically significant, the difference between the two sample statistics will have to have
important consequences in real-life applications. For example, the proportion of people who
developed the flu after the shot was 0.16, and after the nasal spray – 0.24. The difference

STATISTICS FINAL EXAM ESSAYS

4

constituted about 8% of those vaccinated. Though this seems to be a non-negligible figure, it is
still unclear whether this difference will play a role in which vaccination method is preferred by
the majority of patients and their doctors. Both methods seem to yield a low percentage (far
below 50%) of flu cases, and one may be more economic and comfortable to adm...

Daria4117 (1685)
UIUC
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