Answered: How many pairs of shoes, on average, do…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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How many pairs of shoes, on average, do female teens have? To find out, an AP®® Statistics class selected an SRS of 20 female students form their school. Then they recorded the number of pairs of shoes that each student reported having. This class also asked an SRS of 20 boys at their school how many pairs of shoes they have. A 95% confidence interval for ??−??=μG−μB= the true difference in the mean number of pairs of shoes for girls and boys is 10.9 to 26.5.

Interpret the confidence interval.

We are 95% confident that the interval from 10.9 to 26.5 captures the true difference (Girls – Boys) in the mean number of pairs of shoes owned by all girls and boys at this school.

We are 95% confident that the interval from 10.9 to 26.5 captures the true mean difference (??????−????)(μGirls−Boys) in the number of pairs of shoes owned by all girls and boys at this school.

Girls at this school have between 10.9 and 26.5 more pairs of shoes than boys 95% of the time.

We are 95% confident that the interval from 10.9 to 26.5 captures the difference (Girls – Boys) in the mean number of pairs of shoes owned by girls and boys in the sample.

It we were to select many random samples of students at this school and construct a 95% confidence interval using each sample, about 95% of the intervals would capture the true difference (Girls – Boys) in mean number of pairs of shoes owned by all girls and boys at this school.

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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