An experiment is conducted to examine the susceptibility of root stocks of a variety of lemon trees to a specific larva. Thirty of the plants are subjected to the larvae and examined after a fixed period of time. The response of interest is the logarithm of the number of larvae per gram that is counted on each root stock. For these 30 plants, the sample mean is 9.02 and the standard deviation is 1.12.

a) Calculate a 95% confidence interval for , the mean susceptibility for the population of lemon tree root stocks. [4 marks]

b) What would happen to the width of the confidence intervals if the level of confidence of each interval is increased from 95% to 99%? [1 mark]

c) What would happen to the width of the confidence interval if the number of sample was increased from 30 to 100? [1 mark]

d) Test the hypothesis that H₀: =10 versus H_a: 10 and make concluding using level of significance = 0.05. [4 marks]