Answer to Question #183455 in Statistics and Probability for Julie calza

Question

A psychologist believes that it will take at least an hour for certain disturbed 

children to learn a task. A random sample of 30 of these children results in a 

mean of 50 minutes to learn the task. Should the psychologist modify her belief 

at the 0.01 level if the population standard deviation can be assumed to be 15

minutes?

Answer 1

M = 50

Z = 2.58

s_M = $\sqrt{(15^2/30)}$ = 2.74

μ = M ± Z(s_M)

μ = 50 ± 2.58$\times$2.74

μ = 50 ± 7.05 (Lower limit is 50 - 7.05 = 42.95, which is more than 30 minutes)

Answer: the belief that children need more than 30 minutes should not be modified, as they need at least 42.95 minutes.