Answered: nutritionist claims that children 13 to…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

A nutritionist claims that children 13 to 15 years old are consuming less than the recommended iron intake of 20.5 milligrams. A random sample of 50 children 13 to 15 years old was obtained and their daily consumption of
iron was measured. The mean daily iron intake among these children was found to be 12.5 milligrams. Assume that the data for iron intake follows a normal distribution with a standard deviation of 4.75 milligrams.

Construct a 99% confidence interval for the true mean iron intake among children 13 to 15 years old.
Based on the results in #1, is there evidence to support the claim of the nutritionist? Justify your answer.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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