The purpose of the Exam is to assess your understanding of the main statistical conceptscovered in this course. Part I includes three essay questions. All ofyour responses should be included in a single Word document forsubmission. Please include thefollowing general headings for each section of the written exam within yourWord document:Part I: Essay Questions1. Essay 12. Essay 23. Essay 3Part I: Essay QuestionsThere are three essay questions in this section. You must answer all three questions. The length of each essay should be one to twodouble-spaced pages (excluding title and reference pages). Use 12-point font and format your paper withregular 1-inch margins. Do not includethe essay prompt in your document. Itwill not count toward the length requirement for your essays.Essay 1A group of researchers conducted an experiment to determinewhich vaccine is more effective for preventing getting the flu. They tested twodifferent types of vaccines: a shot and a nasal spray. To test theeffectiveness, 1000 participants were randomly selected with 500 people gettingthe 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 thenasal spray, 120 people developed the flu and 380 did not. The level ofsignificance was set at .05. The proportion of people who were treated with theshot who developed the flu = .16, and the proportion of the people who weretreated 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 aresearch study. Interpret thestatistical results and examine the limitations of the statistical methods. Finally, evaluate the research study as awhole and apply what you have learned about hypothesis testing and inferentialstatistics by discussing how you might conduct a follow-up study.Your essay must address the following points: •Describe the research question for this experiment. ◦Whatwere 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 nullhypothesis? •Do the results provide sufficient evidence to support thealternative 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 thisone. Explain your answer. •Describe the difference between practical and statisticalsignificance. Essay 2A researcher has investigated the relationship between IQand grade point average (GPA) and found the correlation to be .75. For this essay, critique the results and interpretation of acorrelational study. •Evaluate the correlational result and identify the strengthof the correlation. •Examine the assumptions and limitations of the possibleconnection between the researcher’s chosen variables. • Identify and describe other statistical tests that couldbe used to study this relationship. Your essay response must address the following questions: •How strong is this correlation? ◦Is this a positive ornegative correlation? ◦What does this correlation mean? •Does this correlation imply that individuals with highIntelligence Quotients (IQ) have high Grade Point Averages (GPA)? • Does this correlation provide evidence that high IQ causesGPA 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 thiscorrelation? •Is correlation a good test for predicting GPA? ◦ If not, what statistical tests should aresearcher use, and why? Essay 3A researcher has recorded the reaction times of 20individuals on a memory assessment. The following table indicates theindividual times:2.2 4.7 7.3 4.19.5 15.2 4.3 9.52.7 3.1 9.2 2.98.2 7.6 3.5 2.59.3 4.8 8.5 8.1In this essay, demonstrate your ability to organize datainto meaningful sets, calculate basic descriptive statistics, interpret theresults, and evaluate the effects of outliers and changes in thevariables. You may use Excel, one of themany free online descriptive statistics calculators, or calculate the values byhand and/or with a calculator. Next, separate the data into two groups of 10; one groupwill be the lower reaction times, and the second group will be the higherreaction times. Then, address thefollowing 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 datapoints in each group. You will have atotal of 20 data points for each group. After completing this, address thefollowing 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?