A pH level of the soil between 5.3 and 6.5 is optimal for strawberries. To measure the pH level, a field is divided into two lots. In each lot, we randomly select 20 samples of soil. The data are below:
pH (lot 1) pH (lot 2)
5.66 5.25
5.73 6.73
5.68 6.25
5.77 5.21
5.73 5.63
5.71 6.41
5.68 5.89
5.58 6.76
6.11 5.13
5.37 5.64
5.67 5.94
5.53 6.16
5.59 5.64
5.94 6.54
5.84 5.79
5.53 5.91
5.64 6.17
5.73 6.90
5.30 5.76
5.65 6.07
(a) Using a statistical software, verify the assumption that the two populations are normally distributed.
(b) Using a statistical software, assess the assumption that the two populations have equal variances.
(c) Test the hypothesis H0 : mu1 = mu2 versus H1 : mu1 neq mu2, where mu1 is the mean pH level of the soil in lot 1, and mu2 is the mean pH level of the soil in lot 2. State your conclusion. Use the level alpha = 0.05