The floor exercise is a commonly shared event between the Women’s and Men’s Artistic Gymnastics programs. Let’s compare the floor exercise scores of the female gymnasts and male gymnasts. To do this, we will consider the 2007, 2011, and 2015 results as sample data. Part B: Apparatus Finals Let’s now look at the floor exercise scores in the Female Apparatus Finals and in the Male Apparatus Finals. Female Apparatus Finals Score Male Apparatus Finals Score 15.25 14.35 14.85 14.05 14.2 14.05 13.95 13.95 13.65 13.85 13.3 13.4 12.7 12.8 0 11.55 14.6 13.6 14.45 13.4 14.2 13.35 13.55 13.1 13.25 13.1 12.85 13.05 11.8 12.7 11.25 12.4 15 13 14.9 12.7 14.45 12.65 14.3 12.65 13.7 12.6 13.55 12.25 13.45 12.15 13.15 12.05 i. Find the sample mean and sample standard deviation for the floor exercise scores in the Female Apparatus Finals. ii. Find the sample mean and sample standard deviation for the floor exercise scores in the Male Apparatus Finals. iii. Based on statistical data, can we infer at the 5% significance level that female gymnasts have a higher population mean floor exercise score in the Apparatus Finals than male gymnasts? (Hint: Use the results of i. and ii. and apply the t-test for difference of population means).

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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The floor exercise is a commonly shared event between the Women’s and Men’s Artistic Gymnastics programs. Let’s compare the floor exercise scores of the female gymnasts and male gymnasts. To do this, we will consider the 2007, 2011, and 2015 results as sample data.

Part B: Apparatus Finals

Let’s now look at the floor exercise scores in the Female Apparatus Finals and in the Male Apparatus Finals.

Female Apparatus Finals Score	Male Apparatus Finals Score
15.25	14.35
14.85	14.05
14.2	14.05
13.95	13.95
13.65	13.85
13.3	13.4
12.7	12.8
0	11.55
14.6	13.6
14.45	13.4
14.2	13.35
13.55	13.1
13.25	13.1
12.85	13.05
11.8	12.7
11.25	12.4
15	13
14.9	12.7
14.45	12.65
14.3	12.65
13.7	12.6
13.55	12.25
13.45	12.15
13.15	12.05

i. Find the sample mean and sample standard deviation for the floor exercise scores in the Female Apparatus Finals.

ii. Find the sample mean and sample standard deviation for the floor exercise scores in the Male Apparatus Finals.

iii. Based on statistical data, can we infer at the 5% significance level that female gymnasts have a higher population mean floor exercise score in the Apparatus Finals than male gymnasts? (Hint: Use the results of i. and ii. and apply the t-test for difference of population means).

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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