a) The t-test is a very useful parametric statistical test. Explain what the t-test is used for and identify three scenarios where the t-test may be used and support your answer with examples and sketches to support your answers.

b) The analysis of a vitamin C in five different biotechnological processes (P1-P5) of a health food are show in the table below. R1-R6 represents replicated analysis for each process.

Table 2

An ANOVA analysis was performed at p=0.05 based on the data above (Table 2) and the results are presented below (Table 3).

Table 3

From the ANOVA results,

i) Conclude if the differences between processes are significant. Clearly justify your answer.

ii) Conclude if the differences between replicates are significant. Clearly justify your answer.

iii) Explain briefly what is meant by statistical significance based on the p-value assuming a p-alpha value?

Table 2 Run P1 P2 P3 P4 P5 R1 24 14 11 7 19 R2 15 7 9 7 24 R3 21 12 7 4 19 R4 27 17 13 7 15 R5 33 14 12 12 10 R6 23 16 18 18 20 An ANOVA analysis was performed at p=0.05 based on the data above (Table 2) and the results are presented below (Table 3). Table 3 ANOVA Source of Variation SS df MS F P-value F crit ROWS 152.1667 5 30.43333 1.502881 0.233412 2.71089 Columns 803 4 200.75 9.91358 0.000137 .2.866081 Error 405 20 20.25 Total 1360.167 29