Question

You have just completed a study of TV viewing in your community. The mean viewing time for TV watched yesterday for a random sample of 400 viewers was 164 minutes. The sample standard deviation was 85 minutes. What is 95% confidence interval for the community’s mean viewing time?

Answer 1

Answer)

As the population s.d is not given and we are using the sample s.d as the best estimate we will use t distribution to estimate the interval

N = 400

Mean = 164

S.d = 85

Degrees of freedom is = n-1 = 399

For 399 dof and 95% confidence level, critical value t from t distribution is = 1.97

Margin of error (MOE) = t*s.d/√n = 1.97*85/√400 = 8.36

Interval is given by

(Mean - MOE, Mean + MOE)

[155.64, 172.36].

You can be 95% confident that the population mean (μ) falls between 155.64 and 172.36.