Question

Suppose that we know from a recent nationwide study that the average American watches 15 hours of television per week with a population standard deviation of 4 hours. Assume that the distribution of the number of hours watched is normal.  Suppose that we randomly select 500 New Orleans residents and measure their average viewing hours are calculated as 24 hours. Use an appropriate statistical test to determine whether New Orleans residents differ from other Americans in terms of the number of hours of television that they watch per week. Complete this problem by hand.

Answer 1

Let denotes the true average viewing hours for New Orleans residents.

To test against

Here

sample mean

population standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of the test statistic =

and p-value

Since P-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that New Orleans residents significantly differ from other Americans in terms of the number of hours of television that they watch per week