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
* ( 
/
= 2.576 * ( 7.1 /
= 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.
orchestra answered 1 year agoRelated Solutions
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