Refer to the attached "Project Template" and "Project Data Generator" documents to complete this project.

The Word document is where you will write all your responses. The Excel file generates your personalized dataset and is used for all required calculations and statistical analyses. Both files are essential for completing the assignment.

Project Data Generator:

Participant ID	Reaction Time (Before)	Reaction Time (After)	Difference (Before-After)
P001	0.503	0.422	0.081
P002	0.772	0.746	0.026
P003	0.667	0.612	0.055
P004	0.61	0.517	0.093
P005	0.557	0.525	0.032
P006	0.485	0.425	0.06
P007	0.739	0.615	0.124
P008	0.655	0.617	0.038
P009	0.6	0.534	0.066
P010	0.545	0.541	0.004
P011	0.463	0.419	0.044
P012	0.716	0.643	0.073
P013	0.644	0.627	0.017
P014	0.59	0.541	0.049
P015	0.533	0.452	0.081
P016	0.43	0.404	0.026
P017	0.698	0.643	0.055
P018	0.633	0.541	0.092
P019	0.58	0.548	0.032
P020	0.52	0.46	0.06
P021	0.332	0.209	0.123
P022	0.683	0.645	0.038
P023	0.622	0.556	0.066
P024	0.569	0.565	0.004
P025	0.505	0.461	0.044
P026	0.779	0.706	0.073
P027	0.669	0.652	0.017
P028	0.612	0.563	0.049
P029	0.558	0.477	0.081
P030	0.488	0.463	0.025
P031	0.742	0.687	0.055
P032	0.657	0.565	0.092
P033	0.602	0.57	0.032
P034	0.547	0.487	0.06
P035	0.466	0.344	0.122
P036	0.719	0.681	0.038
P037	0.645	0.579	0.066
P038	0.591	0.587	0.004
P039	0.535	0.491	0.044
P040	0.435	0.362	0.073
P041	0.7	0.683	0.017
P042	0.634	0.585	0.049
P043	0.581	0.5	0.081
P044	0.522	0.497	0.025
P045	0.365	0.31	0.055
P046	0.685	0.593	0.092
P047	0.624	0.592	0.032
P048	0.571	0.511	0.06
P049	0.507	0.385	0.122
P050	0.786	0.748	0.038
P051	0.671	0.605	0.066
P052	0.613	0.609	0.004
P053	0.56	0.516	0.044
P054	0.49	0.417	0.073
P055	0.746	0.729	0.017
P056	0.658	0.609	0.049
P057	0.603	0.522	0.081
P058	0.549	0.524	0.025
P059	0.469	0.414	0.055
P060	0.721	0.629	0.092
P061	0.647	0.615	0.032
P062	0.593	0.533	0.06
P063	0.537	0.416	0.121
P064	0.441	0.403	0.038
P065	0.702	0.636	0.066
P066	0.636	0.632	0.004
P067	0.583	0.539	0.044
P068	0.524	0.451	0.073
P069	0.383	0.366	0.017
P070	0.687	0.638	0.049
P071	0.625	0.544	0.081
P072	0.572	0.547	0.025
P073	0.509	0.454	0.055
P074	0.795	0.703	0.092
P075	0.673	0.641	0.032
P076	0.615	0.555	0.06
P077	0.561	0.441	0.12
P078	0.493	0.455	0.038
P079	0.751	0.685	0.066
P080	0.66	0.656	0.004
P081	0.604	0.56	0.044
P082	0.55	0.477	0.073
P083	0.473	0.456	0.017
P084	0.724	0.675	0.049
P085	0.648	0.567	0.081
P086	0.594	0.569	0.025
P087	0.538	0.483	0.055
P088	0.445	0.353	0.092
P089	0.705	0.673	0.032
P090	0.637	0.577	0.06
P091	0.584	0.465	0.119
P092	0.526	0.488	0.038
P093	0.396	0.33	0.066
P094	0.689	0.685	0.004
P095	0.626	0.582	0.044
P096	0.574	0.501	0.073
P097	0.512	0.495	0.017
P098	0.805	0.756	0.049
P099	0.675	0.594	0.081
P100	0.616	0.591	0.025
P101	0.563	0.508	0.055
P102	0.495	0.403	0.092
P103	0.755	0.723	0.032
P104	0.662	0.602	0.06
P105	0.606	0.487	0.119
P106	0.552	0.514	0.038
P107	0.476	0.41	0.066
P108	0.728	0.725	0.003
P109	0.65	0.606	0.044
P110	0.596	0.523	0.073
P111	0.54	0.524	0.016
P112	0.45	0.401	0.049
P113	0.707	0.626	0.081
P114	0.639	0.614	0.025
P115	0.585	0.53	0.055
P116	0.527	0.435	0.092
P117	0.406	0.374	0.032
P118	0.691	0.631	0.06
P119	0.628	0.51	0.118
P120	0.575	0.537	0.038
P121	0.514	0.448	0.066
P122	0.819	0.816	0.003
P123	0.676	0.632	0.044
P124	0.617	0.544	0.073
P125	0.565	0.549	0.016
P126	0.498	0.449	0.049
P127	0.76	0.68	0.08
P128	0.663	0.638	0.025
P129	0.607	0.553	0.054
P130	0.553	0.462	0.091
P131	0.479	0.447	0.032
P132	0.731	0.671	0.06
P133	0.651	0.533	0.118
P134	0.597	0.559	0.038
P135	0.542	0.476	0.066
P136	0.454	0.451	0.003
P137	0.71	0.666	0.044
P138	0.64	0.567	0.073
P139	0.587	0.571	0.016
P140	0.529	0.48	0.049
P141	0.414	0.334	0.08
P142	0.693	0.668	0.025
P143	0.629	0.575	0.054
P144	0.577	0.486	0.091
P145	0.516	0.484	0.032
P146	0.837	0.777	0.06
P147	0.678	0.561	0.117
P148	0.619	0.581	0.038
P149	0.566	0.5	0.066
P150	0.5	0.497	0.003
P151	0.765	0.721	0.044
P152	0.665	0.593	0.072
P153	0.609	0.593	0.016
P154	0.555	0.506	0.049
P155	0.482	0.402	0.08
P156	0.734	0.709	0.025
P157	0.653	0.599	0.054
P158	0.598	0.507	0.091
P159	0.543	0.511	0.032
P160	0.458	0.398	0.06
P161	0.712	0.595	0.117
P162	0.642	0.604	0.038
P163	0.588	0.522	0.066
P164	0.531	0.528	0.003
P165	0.422	0.378	0.044
P166	0.695	0.623	0.072
P167	0.631	0.615	0.016
P168	0.578	0.529	0.049
P169	0.518	0.438	0.08
P170	0.873	0.848	0.025
P171	0.68	0.626	0.054
P172	0.62	0.529	0.091
P173	0.567	0.535	0.032
P174	0.502	0.442	0.06
P175	0.771	0.655	0.116
P176	0.667	0.629	0.038
P177	0.61	0.544	0.066
P178	0.557	0.554	0.003
P179	0.484	0.44	0.044
P180	0.738	0.666	0.072
P181	0.655	0.639	0.016
P182	0.6	0.551	0.049
P183	0.545	0.465	0.08
P184	0.462	0.437	0.025
P185	0.715	0.661	0.054
P186	0.643	0.552	0.091
P187	0.59	0.558	0.032
P188	0.533	0.473	0.06
P189	0.428	0.312	0.116
P190	0.697	0.659	0.038
P191	0.632	0.566	0.066
P192	0.579	0.576	0.003
P193	0.52	0.477	0.043
P194	0.318	0.246	0.072
P195	0.682	0.666	0.016
P196	0.622	0.573	0.049
P197	0.569	0.489	0.08
P198	0.505	0.48	0.025
P199	0.777	0.723	0.054
P200	0.669	0.578	0.091

MAT-274 Caffeine and Reaction Time Project

Project Instructions:

You are investigating whether caffeine affects reaction time in college students. Each participant was tested before and after consuming caffeine. Data is uniquely generated from your name (entered in cell B1) and cannot be modified. Answer the following questions using your Excel analysis.

Additionally, as part of this assignment, reflect on how a Christian worldview might influence the interpretation of this research, ethical considerations in experimentation, and the stewardship of health.

Study Design and Context

1. Explain why this is a paired study instead of a two-sample independent design.

1. State two benefits of using a within-subject (paired) design in this context.

1. Identify one potential source of variability that the paired design helps control.

1. Faith Integration: From a Christian perspective, describe how the principle of stewardship over one's body (1 Corinthians 6:19-20) might influence the ethical considerations in conducting studies involving caffeine consumption.

Data Summary

1. Calculate and report the mean, median, and standard deviation of:

• Reaction Time Before Caffeine
• Reaction Time After Caffeine
• Differences (Before - After)

1. Describe what a positive difference means in this study.

1. Based on the summary stats, describe what general trend you observe.

1. Faith Integration: Considering that our bodies are "fearfully and wonderfully made" (Psalm 139:14), describe how this statistical investigation might help us better understand and responsibly care for the way our bodies respond to substances like caffeine.

Visual Analysis

1. Create side-by-side boxplots comparing before and after reaction times.
3. Describe what the boxplots show about:

• Median shift
• Spread
• Skewness
• Outliers

2. Create a scatterplot:

• x-axis: reaction time before
• y-axis: reaction time after
• Add a diagonal line of equality (y = x)
• Interpret the plot

2. Faith Integration: Describe how responsibly used visual data representations can reflect honesty and integrity in reporting scientific findings, in alignment with the teachings of Proverbs 12:22.

Hypothesis Testing

1. Write the null and alternative hypotheses (in symbols and in words).

1. Conduct a paired t-test using Excel:

• t-statistic
• degrees of freedom
• p-value

1. At ?? = 0.05, explain your decision.

1. Explain what this means about caffeine's effect in this sample.

1. Faith Integration: Describe how a Christian should approach conclusions drawn from data, considering the call to seek truth (John 8:32). Identify what cautions should be taken to avoid misinterpreting or overstating statistical findings.

Confidence Interval

1. Calculate a 95% confidence interval for the mean difference (Before - After).

1. Determine if the value 0 is inside your interval.

1. Interpret the confidence interval in context and explain what it suggests.

1. Faith Integration: Describe how understanding statistical uncertainty reminds us of human limitations in knowledge and encourages humility (Proverbs 3:5-6) when interpreting research findings.

Outlier Detection and IQR

1. Use the IQR method on the difference column (Before - After):

• Find Q1, Q3, and IQR
• Identify any outliers

1. Identify how many participants had unusually large or small changes in reaction time.
4. Explain what effect outliers might have on your test results.
6. Faith Integration: Describe what ethical responsibilities researchers have to honestly report unusual findings, and how this aligns with biblical principles of honesty and integrity (Colossians 3:23-24).

Data Quality and Reliability

1. Suggest two ways that measurement errors or experimental conditions could affect this data in real life.

1. Describe what steps you would recommend to improve data reliability if this experiment were repeated with real students.

1. Faith Integration: Describe how striving for accuracy and reliability in research reflects the Christian value of excellence and doing work as unto the Lord (Colossians 3:23).

Interpreting the Results in Context

1. Based on your hypothesis test and confidence interval, summarize whether caffeine appears to have a statistically significant effect on reaction time.

1. Explain whether the observed difference in means is substantial enough to have a meaningful impact in real-world contexts such as driving, athletics, or test-taking.
3. Suppose the standard deviation of the difference scores were much higher.

• Describe how this would affect your confidence interval and hypothesis test.
• Explain if you be confident in your conclusion.

1. Faith Integration: Describe how Christians should use such scientific findings responsibly when making lifestyle choices (e.g., regarding caffeine consumption), keeping in mind self-control as a fruit of the Spirit (Galatians 5:22-23).