A random sample of n = 12 four-year-old red pine trees was selected, and the diameter (in inches) of each tree's main stem was measured. The resulting observations are given below. 11.6 10.4 12.7 15.2 10.8 12.8 16.2 10.1 11.7 11.0 10.4 12.0 (a) Calculate a point estimate of σ, the population standard deviation of main stem diameter. (Round your answer to three decimal places.) σ = inches What statistic did you use to obtain your estimate? sample proportion sample mean sample variance sample range sample standard deviation (b) Suppose that the diameter distribution is normal. Then the 90th percentile of the diameter distribution is μ + 1.28σ (so 90% of all trees have diameters less than this value). Calculate a point estimate for this percentile. (Hint: First calculate an estimate of μ and then use it along with your estimate of σ from part (a). Round your answer to three decimal places.) μ + 1.28σ = inches
A random sample of n = 12 four-year-old red pine trees was selected, and the diameter (in inches) of each tree's main stem was measured. The resulting observations are given below.
11.6
10.4
12.7
15.2
10.8
12.8
16.2
10.1
11.7
11.0
10.4
12.0
(a)
Calculate a point estimate of σ, the population standard deviation of main stem diameter. (Round your answer to three decimal places.)
σ =
inches
What statistic did you use to obtain your estimate?
sample proportion
sample mean
sample variance
sample
sample standard deviation
(b)
Suppose that the diameter distribution is normal. Then the 90th percentile of the diameter distribution is μ + 1.28σ (so 90% of all trees have diameters less than this value). Calculate a point estimate for this percentile. (Hint: First calculate an estimate of μ and then use it along with your estimate of σ from part (a). Round your answer to three decimal places.)
μ + 1.28σ =
inches
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