1. A study was conducted to test the effect of fertilizer and irrigation on tomato crop yield. Two types of fertilizers (Fertilizer A and Fertilizer B) and five levels of irrigation (100, 150, 200, 250, and 300 mm) were applied. For each combination of these factors, 5 replicate plots of tomatoes of the same variety were grown, making a total of 50 plots. The plots in the field were assigned randomly and independently to the combinations of treatments. When the crop matured, the yield of tomatoes in each plot was recorded in kg/m2 .

(a) (1 mark): Identify the study units.

(b) (3 marks): What is/are the explanatory variable(s) or factor(s)? State the type of data scale used (e.g., categorical, ordinal, etc.) for recording the explanatory variable(s).

(c) (2 marks): What is/are the response variable(s)? State the type of data scale used (e.g., categorical, ordinal, etc.) for recording the response variable(s).

(d) (2 marks): Is this an observational or experimental study? Very briefly explain your answer

(e) (4 marks): Based on this study, will it be possible to make either population inferences or causal inferences or both? Briefly explain your answer.

2. .Marcus Brody owns a large museum containing historical artifacts. When doing inventory one year, he calculated that the mean value of ALL items in the museum was $US 10,000. A new employee knows Marcus doesn't have the greatest memory, so taking a random sample of 16 items he reported a 90% confidence interval for the average price to be (9392.050, 9917.950). Assume all the required assumptions are satisfied.

Parameter Uy = average price in $US

a) (1 mark) What is the critical value used in this confidence interval?

b) (2 marks) What is the sample mean from this sample?

c) (2 marks) What is the sample standard deviation from this sample?

d) (1 mark) Based on the confidence interval given in the question, do you think that Marcus' claim is incorrect? Explain the logic of your answer.

e) (5 marks) Is there sufficient evidence, at the 1% significance level, to conclude that Marcus' claim is incorrect? Carry out the most appropriate test. f) (2 marks) Compare your answers in parts (d) and (e) and explain why these either gave you the same conclusion or different conclusions.