(a) Test at the 1% significance level whether the mean arterial blood pressure of all children of diabetic mothers is above 85 mm Hg. (8 marks) (b) What is the P-value of the hypothesis test in part (a)? (2 marks) (c) Obtain and interpret a 90% two-sided confidence interval for the population mean arterial blood pressure of all children of diabetic mothers. (6 marks) (d) Obtain and interpret a 95% two-sided confidence interval for the population mean arterial blood pressure of all children of diabetic mothers. (6 marks) (e) Compare the confidence intervals obtained in parts (c) and (d). Which interval is wider? Write a sentence to summarize the relationship between the length of a confidence interval and the confidence level. (4 marks) (f) State the Type I and Type II errors in the context of this application. (4 marks) 7. The mean retail price of agriculture books in 2005 was $57.61. This year's retail mean price for 28 randomly selected agriculture books was $54.97. Assume that retail price of agriculture books is normally distributed with a population standard deviation of $8.45. (a) At the 5% significance level, do the data provide sufficient evidence to conclude that this year's mean retail price of agriculture books has changed from the 2005 mean? (8 marks) (b) What is the P-value of the test in part (a)? (2 marks)