Question

[15 pts] Ukojaftor is the manager of a tree nursery. He measures the heights of 39 seedlings and obtains a mean of 58.5 cm with a standard deviation of 4.3 cm. a) Construct a 95% confidence interval for these sample seedlings. b) Find the margin of error for the 95% confidence interval for the mean heights of all trees seedlings. c) |Use information from part a to fill in the following sentence: of all samples of size have sample means within of the population mean.

Answer 1

Here the underlying population is assumed to be a normal distribution, to calculate the proper confidence interval.

The detailed solution is given in the pictures below.

Please go through them carefully specially the notations.

Hope the solution helps. Thank you.

(Please do comment if further help is required)

have a e of an then given ny) Plt where tatzant >t a. nru 2 2 x=0.05 ha we know that if we sample of size from a normal distribution and observe sample mean and standard deviation to be in and s respectively, (2-x) x 100% confidence interval is by (x - st nt at in on-l in An- is such that nt) x, not (a) Here and from table we = 39, n = 5815, s=4.3 0.025, 38 957, confidence interval = (57.088 =157.088, 59.912 Aus 6) Margin of error =t1.4 12 Ans in 0.025,38 c) (1-x) x 1007. confidence interval is interpretated (a=0.05 : 95% of all samples of size 39 have sample means within 11412 of the population mean (as this is how margin of exporp is interpretated) get t = 2.024. st