Math Problem Statement

A toy manufacturer wants to see how long, on average, a new toy captures children's attention. He tests 14 children selected at random and finds that their mean attention span is minutes with a standard deviation of 24 minutes. If we assume that attention spans are normally distributed, find a 95% confidence interval for the mean attention span of children playing with this new toy. Give the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Confidence Intervals
Normal Distribution
T-distribution

Formulas

Confidence Interval = x̄ ± t_(α/2) * (s / √n)
Degrees of freedom: df = n - 1

Theorems

Central Limit Theorem
Properties of the t-distribution

Suitable Grade Level

Grades 11-12 or College Level