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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