To study the growth of pine trees at an early stage, a nursery worker records 40 measurements of the heights (cm) of one-year-old red pine seedlings all grown under identical conditions. The 40 heights are given here and are also in heights . csv. 2.6,1.9,1.8,1.6,1.4,2.2,1.2,1.6,1.6,1.5,1.4,1.6,2.3,1.5,1.1,1.6,2.0,1.5,1.7,1.5, 1.6,2.1,2.2,1.0,1.2,1.2,1.8,1.7,0.8,1.5,2.0,2.2,1.5,1.6,2.2,2.1,1.6,1.7,1.7,1.2 (a) Provide point estimatesfor pH, the average height of one-yearold red pine seedlings raised in this nursery and 0H, the standard deviation of the height of one-year-old red pine seedlings raised in this nursery. (b) What is the estimated standard error for X? (0) Construct and interpret a large sample 2 95% condence interval for pH, the average height of one-yearold red pine seedlings raised in this nursery from this sample of 40. Current advertising lists average height of one-year old seedlings as 1.5 cm, does this condence interval suggest they need to update their advertising? (d) Construct (by hand) a 95% t CI for mg, the average height of one-yearold red pine seedlings raised in this nursery from this sample of 40. (e) Which of the following four interpretations of our 95% CI is correct? Explain why it is correct and why the others are wrong. i. 95% of all one-yearold red pine seedlings heights from this nursey have heights between 1.54 cm and 1.79 cm. ii. In a future sample of 40 seedlings, the sample mean height will fall in the interval between 1.54 cm and 1.79 cm. iii. The interval 1.54 cm and 1.79 cm has a probability of 0.95 of containing the mean one-yearold red pine seedlings heights from this nursey. iv. The interval 1.54 cm and 1.79 cm was constructed in such a way that 95% of intervals that could have been constructed would cover the mean height of all seedlings in the nursery. . Consider the 01s for the red pine seedlines built in problem 4. (a) What sample size n is required to reduce the margin of error of a 95% CI to 0.10? (if we are collecting a SRS of independent draws from this population and weassume OH = 0.387). (b) What sample size n is required to reduce the margin of error of a 98% CI to 0.10? (if we are collecting a SRS of independent draws from this population and weassume OH = 0.387). (c) What sample size n is required to reduce the margin of error of a 95% CI to 0.05? (if we are collecting a SRS of independent draws from this population and weassume OH = 0.387). (d) What sample size n is required to reduce the margin of error of a 98% CI to 0.05? (if we are collecting a SRS of independent draws from this population and weassume OH = 0.387)