Suppose I am interested in annual growth rate of mature ponderosa pine trees. I

Question

Suppose I am interested in annual growth rate of mature ponderosa pine trees. I sample 121 iid trees over the course of the year and obtain a sample average growth rate of 18 inches. I noticed there was significant variability in the sampled values, so I construct a 95% confidence interval around my sample mean. This 95% confidence interval is (12, 24). For each of the following interpretations below, determine if they are factual. If they are incorrect, try to explain why. a. 95% of the sampled trees had a growth rate between 12 and 24 inches per year. b. There is a 95% probability the true annual growth rate is between 12 and 24 inches. c. If I sampled trees repeatedly, 95% of the confidence intervals constructed around the sample mean such as the interval (12, 24) would contain the true annual growth rate. d. We are 95% confident the true annual growth rate is between 12 and 24 inches.

Explanation / Answer

95% CI for sample mean is (12,24) means that there is a 95% of the times , the population mean would lie in the interval.

Hence a) says about the sampled trees but doesnt say anything about the mean. Hence False.

b)This is exactly what CI means.

c)This is just opposite of what CI means. It should have been that 95% of the times the population mean would be in the interval.

d)It is again similar to b)

Hence Ans->b),d)

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