Problem 1: A large sample of 100 heights of male students. X_bar = 67.45 inches.
ID: 3218712 • Letter: P
Question
Problem 1:
A large sample of 100 heights of male students.
X_bar = 67.45 inches.
S = 2.93 inches.
Find the 99% confidence interval for the mean height.
Write it in the form: 67.45 +/- ...
Problem 2:
A small sample of only 16 heights of male students.
S = 2.40 inches.
Find the 95% confidence interval for the standard deviation.
Write it in interval form: ( ... , ... )
Problem 3:
Diameter of a sphere. A small sample with 10 measurements.
X-bar = 4.38 inches.
S = 0.06 inches.
Find the 99% confidence interval for the mean diameter.
Write it in the form 4.38 +/- ...
Problem 4:
A sample of 40 pulsars. Of those, 24 were found to spin up
(rotate faster as time goes on), and 16 are spinning down.
The proportion of spinning-up pulsars then is P = 24/40 = 0.6.
Find the 95% confidence interval for the "spin-up" proportion P.
Write your result in the form 0.6 +/- ...
Explanation / Answer
1. Here n is 100 which is pretty large so we will use z distribution
z value for 99% CI is 2.58 as P(-2.58<z<2.58)
Now Margin of error=z*sd/sqrt( n)=2.58*2.93/10=0.75594
Hence CI=mean+/-Margin of error=67.45+/-0.75594