MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Study on Effects of Relaxant on Sleep Onset Time** **Overview:** A study was conducted on a sample of 12 men to test the effects of a relaxant on the time required to fall asleep. The table below displays the number of minutes required for each subject to fall asleep with and without the relaxant. The study uses a 0.05 level of significance to determine if the relaxant reduces the median time needed to fall asleep. **Data Table:** | Subject | Without Relaxant | With Relaxant | |---------|------------------|---------------| | 1 | 15 | 10 | | 2 | 22 | 12 | | 3 | 18 | 10 | | 4 | 8 | 4 | | 5 | 7 | 5 | | 6 | 10 | 7 | | 7 | 17 | 12 | | 8 | 22 | 14 | | 9 | 8 | 6 | | 10 | 10 | 7 | | 11 | 12 | 9 | | 12 | 9 | 8 | **Hypotheses:** a. **Null and Alternative Hypotheses:** - **H₀ (Null Hypothesis):** Median time without Relaxant - Median time with Relaxant ≤ 0 - **H₁ (Alternative Hypothesis):** Median time without Relaxant - Median time with Relaxant > 0 **Statistical Analysis:** b. **Mean and Standard Deviation:** - **Mean of the data:** 39 (Correct) - **Standard Deviation:** 12.75 (Incorrect) **Testing Results:** - **Test Statistic Value:** 10.5 (Incorrect) - **p-value for Hypothesis Test:** 0.0127 (Correct) This study attempts to determine the effectiveness of a relaxant in reducing the time required to fall asleep using statistical analysis, including hypothesis testing.
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Transcribed Image Text:**Study on Effects of Relaxant on Sleep Onset Time** **Overview:** A study was conducted on a sample of 12 men to test the effects of a relaxant on the time required to fall asleep. The table below displays the number of minutes required for each subject to fall asleep with and without the relaxant. The study uses a 0.05 level of significance to determine if the relaxant reduces the median time needed to fall asleep. **Data Table:** | Subject | Without Relaxant | With Relaxant | |---------|------------------|---------------| | 1 | 15 | 10 | | 2 | 22 | 12 | | 3 | 18 | 10 | | 4 | 8 | 4 | | 5 | 7 | 5 | | 6 | 10 | 7 | | 7 | 17 | 12 | | 8 | 22 | 14 | | 9 | 8 | 6 | | 10 | 10 | 7 | | 11 | 12 | 9 | | 12 | 9 | 8 | **Hypotheses:** a. **Null and Alternative Hypotheses:** - **H₀ (Null Hypothesis):** Median time without Relaxant - Median time with Relaxant ≤ 0 - **H₁ (Alternative Hypothesis):** Median time without Relaxant - Median time with Relaxant > 0 **Statistical Analysis:** b. **Mean and Standard Deviation:** - **Mean of the data:** 39 (Correct) - **Standard Deviation:** 12.75 (Incorrect) **Testing Results:** - **Test Statistic Value:** 10.5 (Incorrect) - **p-value for Hypothesis Test:** 0.0127 (Correct) This study attempts to determine the effectiveness of a relaxant in reducing the time required to fall asleep using statistical analysis, including hypothesis testing.
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