Answer to Question #186152 in Statistics and Probability for angel

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 of the population standard deviation can be assumed to be 15 minutes? solution

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: 50 - 7.05 = 42.95, it is more than 30 minutes)

Answer: children need more than 30 minutes (at least 42.95 minutes)