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61. Willows in Yellowstone Writers in some fields summarize data by giving xand its standard error rather than xand sx. Biologists studying willow trees in Yellowstone National Park reported their results in a table with columns labeled x+SE. The table entry for the heights of willow trees (in centimeters) in one region of the park was 61.5519.03.The researchers measured a total of23 trees.
(a) Find the sample standard deviation sx for these measurements. Show your work.
(b) Explain why the given interval is not a confidence interval for the mean height of willow trees in this region of the park.

Short Answer

Expert verified

(a) The sample standard deviation sxfor these measurements is 91.2647

(b) The given interval is not a confidence interval because the factor t*is unknown.

Step by step solution

01

Part (a) Step 1 : Given information

A summarize data by giving xand its standard error rather than xand sx. To find the sample standard deviation sx.

02

Part (a) Step 2 : Explanation

The standard deviation is divided by the square root of the sample size to obtain the standard error of the mean: SE=sxn

The Sample size nis 23. The Standard error of mean SEis 19.03Multiply the two sides by nin the equation SE=sxn.

Hence,

s=SEn

=19.0323

=91.2647

Therefore, the standard deviation is 91.2647.

03

Part (b) Step 1 : Given Information

To explain why the supplied interval for the mean height of willow trees in this park region is not a confidence interval.

04

Part (b) step 2 : Explanation

The confidence interval is calculated using the formula xt*E.

The interval in the problem is xE.

And here, t*is unknown.

As a result, the provided interval is not a confidence interval.

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