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The document describes an experiment comparing the dissolving times of Aleve Liquid-Gel and Aleve Caplets. Researchers randomly selected 30 pills from each bottle and measured how long it took each pill to dissolve in simulated stomach conditions. They found the average dissolving time was 884 seconds for Caplets and 261 seconds for Liquid-Gels. A t-test revealed the difference in means was statistically significant, indicating Liquid-Gels dissolve significantly faster than Caplets.

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Aleve Liquid-Gel v. Aleve Caplets Evan Roberts Hannah Basham AP Stats, Per.1
Experimental Design We are testing Aleve Liquid Gels and Aleve Caplets to see if there is a significant difference in the time of dissolving between the two. We are running a two sample t-test for means. We are buying a bottle of 52 count, 200 milligram Liquid Gels and a bottle of 65 count, 200 milligram Caplets.
Experimental Design  We are assigning each pill from the bottle of Liquid Gels a number between 00-51.  Using the random digits function on the calculator, we will select 30 non-repeating numbers disregarding numbers 52-99.  We are assigning each pill from the bottle of Caplets a number between 00-64.  Using the random digits function on the calculator, we will select 30 non-repeating numbers disregarding 65-99.  Once the pills are randomly selected, we will begin testing them by dropping one pill at a time into a 100 mL beaker with 40 mL of 0.2 M HCl and the beaker will be placed on a magnetic stirrer and heated to 40ºC for each trial.
Experimental Design ï‚— As soon as the pill is dropped into the beaker, the stopwatch will be started. ï‚— As soon as the pill is completely dissolved (i.e. you can no longer see it), the timer will be stopped. ï‚— After each trial, the beaker will be cleaned and new HCl will be added to ensure that the conditions are constant. ï‚— Repeat for the Liquid Gels 30 times total, and then again for the Caplets 30 times total. ï‚— Gather results and compare mean times.
Explanation of Data Collection To begin, we poured all the pills out and assigned each one an appropriate number as stated in the design. We began with the Liquid Gels; the pills we used were as follows:49, 47, 07, 26, 21, 38, 02, 17, 51, 10, 41, 11, 19, 00, 48, 05, 28, 44, 50, 14, 06, 37, 15, 01, 43, 32, 12, 36, 16, 04. Each person dissolved 15 Liquid Gel pills by filling a 100 mL beaker with 40 mL of 0.2 M Hydrochloric acid. The acid was heated to 40°C using the hot plate on the magnetic stirrer. For each trial the stirrer was set at a speed of 6. When the pill was dropped in the timer began, and when it was no longer visible the timer was stopped. After each trial, the beaker was clean and the acid replaced.
Explanation of Data Collection The data for the Caplets was collected in the same fashion as the Liquid Gels. The pills selected were as follows: 64, 12, 25, 07, 15, 55, 24, 38, 39, 05, 01, 00, 45, 57, 29, 35, 41, 60, 43, 51, 21, 14, 40, 08, 30, 18, 53, 63, 31, 26. Again each person dissolved and timed half of the pills. The same amount and concentration of Hydrochloric acid was used and was heated to 40°C. The stirring speed was set at 6. The time was recorded in the same manner and after each trial the beaker was cleaned and the acid replaced.
Explanation of Data Collection
Explanation of Data Collection Hydrochloric Acid Magnetic Stirrer / Hot Plate
Data Caplets 827.5 967 871.7 897.4 841.5 838.6 1020 934.2 855.5 983.6 862.4 811.1 872.1 860.9 894.3 903.6 848.8 991.2 811.1 867.2 896 833.7 910.3 879.3 961.2 880.8 829.4 872.5 820.6 888.6 884.4033333 55.02636662 Liquid Gels 196 294.1 214.3 243.9 270.9 293 227.3 352.8 278.2 251 240.5 273.8 201.4 237 288.3 301.2 276.4 207.8 298.3 280.2 207.8 254 307.5 225.3 267.6 288.1 238 279.6 282.1 241.5 260.5966667 36.93661377 Mean Standard Deviation Mean Standard Deviation
Display of Data 0 2 4 6 8 10 Frequency of Dissolving Times for Aleve Caplets (in Seconds) Frequency Dissolving Time (seconds) 5 5 9 5 1 2 1 2
Display of Data 0 2 4 6 8 10 Frequency of Dissolving Times for Aleve Liquid Gels (in Seconds) Frequency Dissolving Time (seconds) 5 2 7 3 9 3 0 1
Analysis of Data The sample mean dissolving time of Aleve Caplets is 884.403 seconds with a sample standard deviation of 55.026 seconds. The distribution moderately skewed right; however, it is consider normal because of the Central Limit Theorem. The sample mean dissolving time of Aleve Liquid Gels is 260.597 seconds with a sample standard deviation of 36.937 seconds. One time appears to be a potential outlier but with further calculations, it is apparent that it is not. The highest point is 352.8 and the point must be greater than 364.75 to qualify as an outlier. The distribution does not appear to be normal, but passes the normality check due to the Central Limit Theorem.
Inference Test: State We wish to test if the mean dissolving time of Aleve Liquid Gels is significantly less than the mean dissolving time of Aleve Caplets in simulated body conditions at the alpha level of 0.01. μ1 = mean dissolving time (in seconds) of Aleve Caplets μ2 = mean dissolving time (in seconds) of Aleve Liquid Gels HO: μ1 – μ2 = 0, the difference in mean dissolving times of Aleve Caplets and Aleve Liquid Gels is zero. HA: μ1 – μ2 > 0, the difference in mean dissolving times of Aleve Caplets and Aleve Liquid Gels is greater than zero.
Inference Test: Plan Randomness Check: The pills were randomly selected using a calculator. Normality Check: n ≥ 30—because there are thirty trials, the data is considered normally distributed due to the Central Limit Theorem. Independence: There are more than 300 Aleve Liquid Gels and 300 Aleve Caplets, so the data satisfies the 10 % rule. Because of the replacement of acid after each trial, the dissolving of one pill is independent from the others. All checks are satisfied; We will perform a two sample t- test for μ1 – μ2.
Inference Test: Do x1 = 884.403 x2 = 260.597 n1 = 30 n2 = 30 S1 = 55.026 S2 = 36.937 α = 0.01 t = t = 51.44, df = 29 p-value < 0.0005
Inference Test: Conclude With the p-value being extremely smaller than 0.0005, it is then smaller than our alpha of 0.01. Therefore we have statistically significant evidence to reject the null hypothesis and conclude that the mean dissolving time of Aleve Liquid Gels is significantly less than the mean dissolving time of Aleve Caplets.
Reflection After performing this experiment, we would agree that we should have originally researched information about pills dissolving more because we originally tested the pills in water at room temperature and the Liquid Gels would not dissolve and the Caplets dissolved slower than they did in simulated body conditions. Trying to perform these trials was a waste of time because we were unable to compare the data because the Liquid Gel pills would not dissolve. Also, if we would have continued, the data show that Caplets dissolved faster, when, in fact, the Liquid Gels dissolve faster.
Reflection Due to this we had to change the design of our experiment, using 40mL of 0.2 M HCl, which is the volume, concentration, and type of acid that is found in a human stomach. Also, we heated the acid to 40°C, close to the internal body temperature. With these conditions, the mean dissolving times of the pills more accurately reflect the actual dissolving time of pills in the body.
Citation of Sources ï‚— http://chemistry.about.com/od/lecturenoteslab1/a/Sto mach-Ph.htm ï‚— http://www.livestrong.com/article/476461-average- amount-of-stomach-acid-in-the-human-stomach/ ï‚— http://www.cruftbox.com/cruft/docs/dissolve.html ï‚— http://www.Aleve.com/

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Stats powerpoint

  • 1. Aleve Liquid-Gel v. Aleve Caplets Evan Roberts Hannah Basham AP Stats, Per.1
  • 2. Experimental Design We are testing Aleve Liquid Gels and Aleve Caplets to see if there is a significant difference in the time of dissolving between the two. We are running a two sample t-test for means. We are buying a bottle of 52 count, 200 milligram Liquid Gels and a bottle of 65 count, 200 milligram Caplets.
  • 3. Experimental Design ï‚— We are assigning each pill from the bottle of Liquid Gels a number between 00-51. ï‚— Using the random digits function on the calculator, we will select 30 non-repeating numbers disregarding numbers 52-99. ï‚— We are assigning each pill from the bottle of Caplets a number between 00-64. ï‚— Using the random digits function on the calculator, we will select 30 non-repeating numbers disregarding 65-99. ï‚— Once the pills are randomly selected, we will begin testing them by dropping one pill at a time into a 100 mL beaker with 40 mL of 0.2 M HCl and the beaker will be placed on a magnetic stirrer and heated to 40ºC for each trial.
  • 4. Experimental Design ï‚— As soon as the pill is dropped into the beaker, the stopwatch will be started. ï‚— As soon as the pill is completely dissolved (i.e. you can no longer see it), the timer will be stopped. ï‚— After each trial, the beaker will be cleaned and new HCl will be added to ensure that the conditions are constant. ï‚— Repeat for the Liquid Gels 30 times total, and then again for the Caplets 30 times total. ï‚— Gather results and compare mean times.
  • 5. Explanation of Data Collection To begin, we poured all the pills out and assigned each one an appropriate number as stated in the design. We began with the Liquid Gels; the pills we used were as follows:49, 47, 07, 26, 21, 38, 02, 17, 51, 10, 41, 11, 19, 00, 48, 05, 28, 44, 50, 14, 06, 37, 15, 01, 43, 32, 12, 36, 16, 04. Each person dissolved 15 Liquid Gel pills by filling a 100 mL beaker with 40 mL of 0.2 M Hydrochloric acid. The acid was heated to 40°C using the hot plate on the magnetic stirrer. For each trial the stirrer was set at a speed of 6. When the pill was dropped in the timer began, and when it was no longer visible the timer was stopped. After each trial, the beaker was clean and the acid replaced.
  • 6. Explanation of Data Collection The data for the Caplets was collected in the same fashion as the Liquid Gels. The pills selected were as follows: 64, 12, 25, 07, 15, 55, 24, 38, 39, 05, 01, 00, 45, 57, 29, 35, 41, 60, 43, 51, 21, 14, 40, 08, 30, 18, 53, 63, 31, 26. Again each person dissolved and timed half of the pills. The same amount and concentration of Hydrochloric acid was used and was heated to 40°C. The stirring speed was set at 6. The time was recorded in the same manner and after each trial the beaker was cleaned and the acid replaced.
  • 7. Explanation of Data Collection
  • 8. Explanation of Data Collection Hydrochloric Acid Magnetic Stirrer / Hot Plate
  • 10. Display of Data 0 2 4 6 8 10 Frequency of Dissolving Times for Aleve Caplets (in Seconds) Frequency Dissolving Time (seconds) 5 5 9 5 1 2 1 2
  • 11. Display of Data 0 2 4 6 8 10 Frequency of Dissolving Times for Aleve Liquid Gels (in Seconds) Frequency Dissolving Time (seconds) 5 2 7 3 9 3 0 1
  • 12. Analysis of Data The sample mean dissolving time of Aleve Caplets is 884.403 seconds with a sample standard deviation of 55.026 seconds. The distribution moderately skewed right; however, it is consider normal because of the Central Limit Theorem. The sample mean dissolving time of Aleve Liquid Gels is 260.597 seconds with a sample standard deviation of 36.937 seconds. One time appears to be a potential outlier but with further calculations, it is apparent that it is not. The highest point is 352.8 and the point must be greater than 364.75 to qualify as an outlier. The distribution does not appear to be normal, but passes the normality check due to the Central Limit Theorem.
  • 13. Inference Test: State We wish to test if the mean dissolving time of Aleve Liquid Gels is significantly less than the mean dissolving time of Aleve Caplets in simulated body conditions at the alpha level of 0.01. μ1 = mean dissolving time (in seconds) of Aleve Caplets μ2 = mean dissolving time (in seconds) of Aleve Liquid Gels HO: μ1 – μ2 = 0, the difference in mean dissolving times of Aleve Caplets and Aleve Liquid Gels is zero. HA: μ1 – μ2 > 0, the difference in mean dissolving times of Aleve Caplets and Aleve Liquid Gels is greater than zero.
  • 14. Inference Test: Plan Randomness Check: The pills were randomly selected using a calculator. Normality Check: n ≥ 30—because there are thirty trials, the data is considered normally distributed due to the Central Limit Theorem. Independence: There are more than 300 Aleve Liquid Gels and 300 Aleve Caplets, so the data satisfies the 10 % rule. Because of the replacement of acid after each trial, the dissolving of one pill is independent from the others. All checks are satisfied; We will perform a two sample t- test for μ1 – μ2.
  • 15. Inference Test: Do x1 = 884.403 x2 = 260.597 n1 = 30 n2 = 30 S1 = 55.026 S2 = 36.937 α = 0.01 t = t = 51.44, df = 29 p-value < 0.0005
  • 16. Inference Test: Conclude With the p-value being extremely smaller than 0.0005, it is then smaller than our alpha of 0.01. Therefore we have statistically significant evidence to reject the null hypothesis and conclude that the mean dissolving time of Aleve Liquid Gels is significantly less than the mean dissolving time of Aleve Caplets.
  • 17. Reflection After performing this experiment, we would agree that we should have originally researched information about pills dissolving more because we originally tested the pills in water at room temperature and the Liquid Gels would not dissolve and the Caplets dissolved slower than they did in simulated body conditions. Trying to perform these trials was a waste of time because we were unable to compare the data because the Liquid Gel pills would not dissolve. Also, if we would have continued, the data show that Caplets dissolved faster, when, in fact, the Liquid Gels dissolve faster.
  • 18. Reflection Due to this we had to change the design of our experiment, using 40mL of 0.2 M HCl, which is the volume, concentration, and type of acid that is found in a human stomach. Also, we heated the acid to 40°C, close to the internal body temperature. With these conditions, the mean dissolving times of the pills more accurately reflect the actual dissolving time of pills in the body.
  • 19. Citation of Sources ï‚— http://chemistry.about.com/od/lecturenoteslab1/a/Sto mach-Ph.htm ï‚— http://www.livestrong.com/article/476461-average- amount-of-stomach-acid-in-the-human-stomach/ ï‚— http://www.cruftbox.com/cruft/docs/dissolve.html ï‚— http://www.Aleve.com/