Children as young as 2 years of age, upon seeing an object placed under a pillow in a familiar setting at home, will understand to look for it after an interval of time and be able to find it. Investigators believe this capability will be less pronounced in a laboratory situation, where the child is away from the familiar setting of home. Let π denote the proportion of 2-year-olds than have this understanding in the home situation, and suppose that π = .35. The investigators wish to determine whether the proportion that remembers is less when the child is away from home.
a) What is the appropriate null hypothesis?
b) What is the appropriate alternative hypothesis?
c) In your own words, distinguish between a Type I and a Type II error in this context.

Question

Children as young as 2 years of age, upon seeing an object placed under a pillow in a familiar setting at home, will understand to look for it after an interval of time and be able to find it. Investigators believe this capability will be less pronounced in a laboratory situation, where the child is away from the familiar setting of home. Let π denote the proportion of 2-year-olds than have this understanding in the home situation, and suppose that π = .35. The investigators wish to determine whether the proportion that remembers is less when the child is away from home. 
a) What is the appropriate null hypothesis? 
b) What is the appropriate alternative hypothesis? 
c) In your own words, distinguish between a Type I and a Type II error in this context.

Quizplus · Accepted Answer

The Answer is a) H₀ : π = .35
b) Ha : π < .35
c) A Type I error is to decide that children remember less when outside of the home environment, when in fact, they remember equally well. A Type II error is to decide that children remember as well in the laboratory setting as in the home setting, when in fact they remember less away from home.

Children as Young as 2 Years of Age, Upon Seeing