Statistical Technique.

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Statistical Technique

The Mann-Whitney U Test will be used as differences between two treatments (two carbohydrates, sucrose and glucose) are being investigated and measurements have been taken at least six times with each treatment. Random sampling will therefore be useful and the data summarised using the median.

Results Table:

This table shows the volume of gas collected in five minutes in cm from each carbohydrate

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As neither starch nor lactose produced any result they shall not be investigated in the statistical test.

Null Hypothesis: there is no difference between the volume of gas produced by sucrose or by glucose.

Ra = 22.5     Na = 6     Nb = 6    Rb = 55.5

Ra + Rb = [(Na + Nb)(Na + Nb + 1)]         =     Ra + Rb = 78

                                    2

Ua = NaNb + Nb(Nb + 1) – Rb             =  Ua = 36 + 21 – 55.5 = 1.5

                                   2

Ub = NbNa + Na(Na + 1) – Ra             =  Ub = 36 + 21 – 22.5 = 34.5

                                 2

Na = 6   Nb = 6   CV = 5                         U         CV

                                                                 1.5  <    5

As the smallest U value is less than the critical value the null hypothesis can be rejected. Therefore it has been statistically proven that there is a difference between the volume of gas produced by sucrose and the volume of gas produced by glucose.

Interpretation of Results

Results Table:

This table shows the volume of gas collected in five minutes in cm from each carbohydrate

.

From this results table and the graph (enclosed) it is clear that glucose produces the greatest volume of carbon dioxide gas and that sucrose produces less gas than glucose but still a significant amount. The starch and the lactose both resisted fermentation producing no carbon dioxide gas in the five minutes timed.

These results can be explained by looking at the shape and chemical composition of the carbohydrate molecules. The table below shows the type of each carbohydrate molecule and its composition.

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Being a monosaccharide glucose is a single sugar unit which is very small and dissolves readily in water.

Sucrose and lactose are carbohydrates classed as disaccharides, they contain two sugar units. They are made when two monosaccharides join together by a reaction when one molecule of water is removed. This is known as a condensation reaction and produces a bond between the two molecules called a glycosidic link. The reaction will also go in the reverse direction, if a molecule of water is added to a disaccharide molecule two monosaccharide ...

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