Question

Let's go to the movies: A random sample of 43 Foreign Language movies made since 2000 had a mean length of 112.5

minutes, with a standard deviation of 12.6 minutes.

Construct a 95% confidence interval for the true mean length of all Foreign Language movies made since

2000. Round the answers to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 112.5

Population standard deviation =    = 12.6

Sample size n =43

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96 * ( 12.6 / 43 )

= 3.8
At 95% confidence interval mean
is,

- E < < + E

112.5 - 3.8 <   < 112.5 + 3.8

108.7 <   < 116.3

( 108.7 , 116.3 )