Answered: An IQ test is designed so that the mean…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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An IQ test is designed so that the mean is 100 and the standard deviation is

for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with

confidence that the sample mean is within

IQ points of the true mean. Assume that

sigma

equals23

and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

The required sample size is

nothing

(Round up to the nearest integer.)

Would it be reasonable to sample this number of students?

This number of IQ test scores is a fairly

large

number.

Yes

This number of IQ test scores is a fairly

large

number.

This number of IQ test scores is a fairly

small

number.

Yes

This number of IQ test scores is a fairly

small

number.

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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