Question

1. Too much TV? A father is concerned that his teenage son is watching too much television each day, since his son watches an average of 2 hours per day. His son says that his TV habits are no different than those of his friends. Since this father has taken a stats class, he knows that he can actually test to see whether or not his son is watching more TV than his peers. The father collects a random sample of television watching times from boys at his son’s high school and gets the following data:

1.9 2.3 2.2 1.9 1.6 2.6 1.4 2.0 2.0 2.2

Is the father right? That is, is there evidence that other boys average less than 2 hours of television per day? Conduct a hypothesis test, making sure to state your conclusions in the context of the problem.

Answer 1

Data:    

n = 10   

μ = 2   

s = 0.3446   

x-bar = 2.01   

Hypotheses:    

Ho: μ ≥ 2   

Ha: μ < 2   

Decision Rule:    

α = 0.05   

Degrees of freedom = 10 - 1 = 9

Critical t- score = -1.833112923   

Reject Ho if t < -1.833112923   

Test Statistic:    

SE = s/√n = 0.3446/√10 = 0.108972088

t = (x-bar - μ)/SE = (2.01 - 2)/0.108972088169402 = 0.091766618

Decision (in terms of the hypotheses):    

Since 0.091766618 > -1.833112923 we fail to reject Ho

Conclusion (in terms of the problem):    

There is no sufficient evidence that other boys average less than 2 hours of television per day.