Question

2. You are interested in the mean number of hours that Americans consume media (watching, reading, listening to content produced by someone else) each day. A random sample of 200 Americans consumes an average of 10.3 hours of media per day, with a standard deviation of 3.5 hours. Construct and interpret a 95% confidence interval for the true mean number of hours that Americans consume media each day.

Answer 1

Solution :

Given that,

= 10.3

s = 3.5

n = 200

Degrees of freedom = df = n - 1 = 200 - 1 = 199

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,199 = 1.972

Margin of error = E = t_/2,df * (s /n)

= 1.972 * (3.5 / 200 )

= 0.5

Margin of error = 0.50

The 95% confidence interval estimate of the population mean is,

- E < < + E

10.3 - 0.5 < < 10.3 + 0.5

9.8 < < 10.8