A research group wanted to verify the results of a previous study done at another research institution in promoting the production of protective factors for rice plants by using a combination of chemicals called Formula XYZ. The previous study reported that the mean concentration of such protective factors after an application of Formula XYZ was 50. The new study examined 15 rice plants and the concentration of protective factors were as follows:

45, 58, 72, 52, 61, 71, 62, 56, 34, 45, 67, 51, 48, 68, 55

a) State the appropriate hypotheses to test whether the concentration of protective factors in the new study were higher than that of the previous study. [2 marks]

b) Determine the mean and standard deviation of the sample of rice plants' concentration of protective factors. [3 marks]

c) Test the hypotheses stated in part (a) at a 5% level of significance, and comment on your findings. [5 marks]