The test results and statistical tests  |
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 t-Test Pineapple juice First compare the mean amount of vitamin C in apple juice (5.58mg) with pineapple juice which has a mean of 4.48. You take the first mean which is apple juice and the next mean which is pineapple juice and find the difference: (X1-X2) = (5.58-4.48) = 1.1 Then the means must individually be divided by the number of samples sqaure rooted. (In this case the square root of 6 which is 2.45) 5.58/2.45 = 2.27 4.48/2.45=1.83 these results are then added to give 4.1. to get the "t" value the difference in means is divided by this value. t= 1.1/4.1= 0.26. To work out the degrees of freedom the total number of samples must be added then minus 2. so 6+6-2 = 10. This value is used to read of the degrees of freedom table. It shows there is over a 20% significance level between grapefruit juice and apple juice. Grapefruit juice Then compare apple juice it with graprefruit juice which has a mean of 3.81mg. You take the first mean which is apple juice and the next mean which is grapefruit juice and find the difference: (X1-X2) = (5.58-3.81) = 1.77 Then the means must individually be divided by the number of samples sqaure rooted. (In this case the square root of 6 which is 2.45) 3.81/2.45 = 1.56 5.58/2.45=2.27 These results are then added to give 3.83. to get the "t" value the difference in means is divided by this value. t= 0.67/3.88= 0.17 To work out the degrees of freedom the total number of samples must be added then minus 2. so 6+6-2 = 10. This value is used to read of the degrees of freedom table. It shows there is over a 20% significance level between grapefruit juice and apple juice. Tomato juice Then compare apple juice it with tomato juice which has a mean of 3.08mg. You take the first mean which is apple juice and the next mean which is grapefruit juice and find the difference: (X1-X2) = (5.58-3.08) = 2.5 Then the means must individually be divided by the number of samples sqaure rooted. (In this case the square root of 6 which is 2.45) 3.08/2.45 = 1.26 5.58/2.45=2.27 These results are then added to give 3.53. to get the "t" value the difference in means is divided by this value. t= 2.5/3.53=0.70 to work out the degrees of freedom the total number of samples must be added the minus 2. so 6+6-2 = 10. this value is used to read of the degrees of freedom table. It shows there is over a 20% significance level between grapefruit juice and apple juice.
Comparing the results obtained with expected results: There is 1g to 1ml. There are 1000mg in a gram so:
Apple juice is expected to have 6mg of vitamin C per 100g. The results gave apple to have 5.58ml of vitamin C per 100ml. Apple juice is expected to have 0.6g per 100g and the results gained show 5.58g per 100g. this is significantly higher
Pineapple juice has an expected value of 15mg of vitamic C per 100g. The results show it had 4.48ml per 100ml. Pineapple juice should have 1.5g per 100g and the results show 4.48g per 100g. The difference is less significant that the results from apple.
Grapefruit juice is expected to have 11mg of vitamin C per 100g. The results show it had 3.81ml per 100ml. Grapefruit juice should have 1.1g per 100g and the results gave a value of 3.81g per 100g. The difference again is less significant than from apple juice.
Tomato juice is expected to have 19mg of vitamin C per 100g. The results show it had 3.08 ml per 100g. Tomato juice should have 1.9g per 100g and the results showed a value of 3.08g per 100g. The difference here is again quite significant. |
The results gained by doing this experiment are in the table above. These results will be used to carry out statistical tests . This will also be done to either prove or disprove my null hypthesis.
The Statistical tests Once the results were obtained it was possible to carry out statisical tests to compare the gained data to one another.The statistical test being carried out is t-test. This is a statistical test used to compare two sets of data by looking at the means. The reason chosen to carry out the t-test is because it is used to compare the means of the data in relation to how the data varies. First look at the null hypothesis. It stated that there would be more vitmain C in apple juice than the others. So i will be comparing the results gained from apple juice to compare individually to each other result. Standard deviation and Standard error First you have to calculate the standard deviation for each fruit . This is done by creating the table labelled table 2.(apple juice) You then work out the sum of x-x squared which is 0.3272. This is then divided by the number of samples minus 1. so: 0.3272/(6-1) = 0.065. The standard deviation calculations for pineapple juice are shown in table 3. The sum of x-x squared is 0.01144. again this is divided by the number of samples: 0.01144/(6-1) = 0.0023. The standard deviation calulations for grapefruit juice are shown in table 4. The sum of x-x squared is 0.1544. this divided by the data amount is : 0.1544/(6-1) = 0.0301 the standard deviation calculations for tomato juice are shown in table 5. the sum of x-x squared is 0.0484. This is divided by the data amount to give: 0.0484/(6-1)= 0.0097 Standard deviation is how the data varies. In this case you are comparing the fruit juices. Standard error is the standard deviation of the how data varies is statistics.
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