Question

A biochemist studying the activity of the enzyme triose phosphate isomerase (TPI) in a species of Drosophila wishes to know if the mean activity of this enzyme is the same at pH = 5 and at pH = 8.

Assuming activities in µM/min are normally distributed, determine if the mean activities of TPI are significantly different at these two pH levels.

pH = 5	11.1	10.0	13.3	10.5	11.3
pH = 8	12.0	15.3	15.1	15.0	13.2

Suppose that you mistakenly believed that the data sets were independent samples taken from two different populations, that is, two different species of Drosophila.

Carry out the t test and determine whether you would have found that female dementia patients who were given bright light and melatonin would have a significantly higher subjective scores for well-being.

Explain the cause of any differences in your results when compared to the previous problem.

Answer 1

First we have performed test for homogeneity.MINITAB shows the following

Test for Equal Variances: pH=5, pH=8

95% Bonferroni confidence intervals for standard deviations

N Lower StDev Upper
pH=5 5 0.705502 1.26016 4.35958
pH=8 5 0.814580 1.45499 5.03361

F-Test (normal distribution)
Test statistic = 0.75, p-value = 0.787

Since p-value is quite high we can easily assume two independent homogeneous normal population.

Now we are going to perform Fisher's t-test.MINITAB shows the following:

Two-sample T for pH=5 vs pH=8

N Mean StDev SE Mean
pH=5 5 11.24 1.26 0.56
pH=8 5 14.12 1.45 0.65

Difference = mu (pH=5) - mu (pH=8)
Estimate for difference: -2.88000
95% CI for difference: (-4.86504, -0.89496)
T-Test of difference = 0 (vs not =): T-Value = -3.35 P-Value = 0.010 DF = 8
Both use Pooled StDev = 1.361

Since p-value<0.05, reject the null and we can conclude that the means are different for two different pH level.