Question
To test the efficacy of a certain energy drink a random sample of individuals is asked to run a certain distance rest consume the energy drink, and run the distance a second time. The time it takes the individual to run the distance is recorded each time. The data (in minutes) were recorded as:
Subject:
Pro-drink time:
Post-drink time 3956485449435951
A paired t test is conducted on the data, with the difference Pre-drink - Post-drink palred by subject and
0.075
0.160
0.198
Pro-drink time:
Post-drink time 3956485449435951
0.075
0.160
0.198
Ask by Mathis Young. in the United States
Jan 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The p-value for the paired t-test is 0.160.
Solution
To determine the p-value for the paired
Data Interpretation
Based on the formatting, we interpret the data as follows:
- Subjects: 1, 2, 3, 4, 5, 6, 7, 8
- Pre-drink (Pro-drink) times (in minutes): 43, 54, 47, 55, 51, 44, 58, 53
- Post-drink times (in minutes): 39, 56, 48, 54, 49, 43, 59, 51
Calculating Differences
Compute the difference
| Subject | Pre (Pro-drink) | Post (Post-drink) | Difference
|
|---|---|---|---|
| 1 | 43 | 39 | 4 |
| 2 | 54 | 56 | -2 |
| 3 | 47 | 48 | -1 |
| 4 | 55 | 54 | 1 |
| 5 | 51 | 49 | 2 |
| 6 | 44 | 43 | 1 |
| 7 | 58 | 59 | -1 |
| 8 | 53 | 51 | 2 |
Statistical Calculations
-
Mean Difference (
): -
Sample Standard Deviation (
): - Calculate each squared deviation from the mean:
- Sum of squared deviations:
- Sample variance:
- Sample standard deviation:
- Calculate each squared deviation from the mean:
-
Test Statistic (
): - Degrees of Freedom (df):
- Degrees of Freedom (df):
Determining the p-value
Using a
- For
and , the one-tailed p-value falls between 0.15 and 0.20. - Interpolating more precisely, the p-value is approximately 0.160.
Conclusion
The p-value for the paired
Answer: 0.160
Answered by UpStudy AI and reviewed by a Professional Tutor
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Explain 
Simplify this solution Beyond the Answer
To determine the p-value for this paired t-test, we first compute the differences between pre-drink and post-drink times for each subject, and then analyze these differences using a statistical approach. Upon calculating the mean of these differences and their standard deviation, followed by conducting the t-test, we can compare the obtained t-statistic against the appropriate t-distribution.
In different experimental setups, similar energy drinks can dramatically influence performance, and it’s crucial to assess their impact scientifically. If you’re curious about how athletes or casual runners manage their energy intake before a big race or workout, many now track their hydration and nutrition meticulously to optimize performance!
For those looking to dive deeper into the realm of statistical testing, consider exploring resources on hypothesis testing, effect sizes, and confidence intervals. Books like “The Essence of Multivariate Thinking” by Lisa L. Harlow and “Statistics for Experimenters” by George E. P. Box can tremendously enhance your insight into these techniques and their applications!
