*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.

Your essay must address the following points:

- 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?
- Was the sample appropriate for this study? Explain your answer.
- What are some possible limitations to this study?
- Discuss how you would conduct a follow up study to this one. Explain your answer.
- 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 researcherâ€™s chosen variables.
- Identify and describe other statistical tests that could be used to study this relationship.

Your essay response must address the following questions:

- 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?