Answered: The owner of a fitness center is…

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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The owner of a fitness center is interested in estimating the difference in mean years that female members have been with the club compared with male members. He wishes to develop a 99% confidence interval estimate. The data are shown in the accompanying table. Assuming that the sample data are approximately normal and that the two populations have equal variances, develop and interpret the confidence interval estimate. Discuss the result.

Gender (1=Male 2=Female)	Years With the Club	Gender (1=Male 2=Female)	Years With the Club
1	4.5	1	5.5
2	1	2	2
1	2.5	2	1.5
2	2	2	3.5
2	3.5	1	4
1	3.5	2	1.5
1	5.5	1	4.5
2	1	1	2
1	2	2	4
2	1.5	1	2
2	3.5	2	2
2	6.5	2	3
1	1.5	1	0
1	3	2	3.5
2	1	2	2
1	3	1	5.5
2	4	1	1
2	1.5	2	3
1	1	2	1.5
2	0	1	1
2	2.5	1	4.5
1	3.5	1	2.5
2	4	1	1
1	5.5	2	5
1	2.5	2	6

The 99% confidence interval for the difference between the two population means for the number of years as members of the fitness club is

?≤(μ1−μ2)≤? explain plz

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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