Question

There is some evidence that suggests that children with obesity watch more TV than children who are not obese. To examine this relationship, researchers obtain a random sample of n = 36 children 6-10 years old, who have been diagnosed as being obese per the BMI chart. Each child is asked to record the number of hours spent each day watching TV. The average for this sample is M = 4.9 hours. It is known that the general population of 6-10 years old children watches an average of μ = 4.1 hours per day, with σ = 1.8 hours.

A.Explain the results of this hypothesis test. Can we conclude that the average child with obesity watches TV for a different amount of time than a non-obese child? If so, do they watch more or less TV? make sure to state if they watch more or less

B. Calculate the estimated effect size the way it was illustrated in the lecture. Would the observed effect size generally be considered small, moderate, or large, explain how you arrived at that decision.

Answer 1

Part a)

H0 :- µ = 4.1
H1 :- µ > 4.1

Test Statistic :-
Z = ( X - µ ) / ( σ / √(n))
Z = ( 4.9 - 4.1 ) / ( 1.8 / √( 36 ))
Z = 2.6667

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Critical value Z(α) = Z(0.05) = 1.645
Z > Z(α) = 2.6667 > 1.645
Result :- Reject null hypothesis

There is sufficient evidence to support the claim that children with obesity watch more TV than children who are not obese.

Part b)

Effect size = ( 4.9 - 4.1 ) / 1.8 = 0.44

There is moderate effect size.

<= 4 small effect size

4 - 6 Moderate effect size

> 6 Large effect size