The American Film Institute discovered that the average American spent 78 hours viewing movies last year based on a study of 50 US people. This sample's standard deviation was nine hours. With the help of this, develop a 95% confidence interval for the population mean number of hours spent watching movies last year.

Solution

VerifiedThe confidence interval for the population mean when the population distribution is normal and the population standard deviation is unknown is given by

$\overline{x}\pm t\cdot\dfrac{s}{\sqrt{n}},$

where $\overline{x}$ is the sample mean which is a point estimate of the population mean, the value of $t$ is found in the Student's $t$ Distribution table for the given confidence level and degrees of freedom, $s$ is the sample standard deviation, and $n$ is the number of observations in the sample.