Attractiveness of body types has been a large discussion relating to effects on youth and culture. Unhealthy levels of BMI are often associated with beauty. A researcher decided to study how young heterosexual adults body type preferences related to BMI. Participants were asked to use a computer program to design their desired partner. The program then calculated the BMI of the designed partners. The table summarizes the results based on a SRS of 35 men and 48 women. BMI designed by menn=35x-bar=18.850stdev=1.750SE Mean 0.277BMI designed by womenn=48x-bar=25.860stdev=4.215SE Mean 0.625Use this information to conduct a test to decide if male and/or female body type preferences are associated with healthy BMI measurements. You should have two complete tests here. You may assume the populations are normally distributed.

BMI designed by men n=35x¯=18.85s=1.75S.E Mean=0.277 BMI designed by women n=48x¯=25.860s=4.215S.E…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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Attractiveness of body types has been a large discussion relating to effects on youth and culture. Unhealthy levels of BMI are often associated with beauty. A researcher decided to study how young heterosexual adults body type preferences related to BMI. Participants were asked to use a computer program to design their desired partner. The program then calculated the BMI of the designed partners. The table summarizes the results based on a SRS of 35 men and 48 women.

BMI designed by men	n=35	x-bar=18.850	stdev=1.750	SE Mean 0.277
BMI designed by women	n=48	x-bar=25.860	stdev=4.215	SE Mean 0.625

Use this information to conduct a test to decide if male and/or female body type preferences are associated with healthy BMI measurements. You should have two complete tests here. You may assume the populations are normally distributed.

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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