Question

A random sample of 32 Hollywood movies made since the year 2000 had a mean length of 111.7 minutes with a standard deviation of 13.8 minutes. Construct a 95% confidence interval for the true mean length of all Hollywood movies made since 2000.

Answer 1

Sample size = n = 32

Sample mean = = 111.7

Sample standard deviation = s = 13.8

We have to construct a 95% confidence interval for the true mean.

Here population standard deviation is unknown so we have to use t-confidence interval.

Formula is

Here E is margin of error

Degrees of freedom = n - 1 = 32 - 1 = 31

Level of significance = 0.05

tc = tα/2,df = t0.025,31 = 2.04

E = 2.04*13.8 / √32 = 4.9766

So confidence interval is (111.7 - 4.9766 , 111.7+4.9766) = (106.72 , 116.68)

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