Question

In: Statistics and Probability

As part of an environmental studies class​ project, students measured the circumferences of a random sample...

As part of an environmental studies class​ project, students measured the circumferences of a random sample of 50 blue spruce trees near Brainard​ Lake, Colorado. The sample mean circumference was 30.4 inches. The population standard deviation is known to be around 7.1 inches. Find a 99% confidence interval for the population mean circumference of all blue spruce trees near this lake.

​A) What type of confidence interval are you to​ find?

A.

​1-Sample Mean Interval using Z

B.

​1-Sample Mean Interval using T

C.

None of the Above

​B) Confidence​ Interval: (

nothing

​,

nothing

​)

​(round each interval limit to two decimal​ places)

​C) Interpret the interval in the SHOW YOUR WORK area.

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 30.4

Population standard deviation =    = 7.1

Sample size = n =50

A) Sample mean interval using Z

B) At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005  = 2.576


Margin of error = E = Z/2 * ( /n)

= 2.576 * ( 7.1 /  50 )

= 2.59

At 99% confidence interval estimate of the population mean is,

  ± E

30.4 ± 2.59   

( 27.81, 32.99 )  

C) We are 99% confident that the true mean circumference of all blue spruce trees near this lake between 27.81 and 32.99 in.


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