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 A: Individual All-Around Finals We will first look at the floor exercise scores in the Individual Female All-Around Finals and in the Individual Male All-Around Finals.Female All-Around Finals Floor ExerciseMale All-Around Finals Floor Exercise1513.5514.8513.7515.213.514.2514.2513.8513.351313.8513.613.513.713.114.0512.812.712.3514.0513.2513.6510.613.2512.613.2513.3513.5513.512.9513.5513.5512.913.0511.811.8513.0513.213.41112.0513.811.0512.2511.812.111.812.111.911.612.3511.912.512.0512.3510.7511.9511.212.0510.5511.611.110.910.4512.59.612.0513.851314.2513.614.813.81412.5514.512.813.751213.5513.512.5512.0513.213.1513.713.2513.3511.813.2512.7512.9512.3513.412.7513.3512.213.312.8512.312.4513.5512.712.812.5512.412.3513.112.2512.312.4512.61312.6512.0511.91210.212.512.0512.211.712.2510.411.8510.7511.959.811.59.611.510.759.79.7510.559.55109.0512.114.6512.8514.212.6515.3512.914.611.814.312.914.7512.4513.6511.9513.712.114.2511.813.812.3514.112.113.6121411.8514.2512.213.211.714.412.1513.2511.313.711.313.1512.413.051213.451212.411.4513.31112.7510.8512.211.2512.610.611.5510.511.610.111.611101110.910.8510.3510.3511.7510.211.311.0510.3 10.9 i. Find the sample mean and sample standard deviation for the floor exercise scores in the Individual Female All-Around Finals.ii. Find the sample mean and sample standard deviation for the floor exercise scores in the Individual Male All-Around Finals.iii. Construct a 95% confidence interval for the difference in population mean floor exercise scores between female and male gymnasts in the Individual All-Around Finals. (Hint: Use the results of i. and ii. and use the t-distribution.)iv. Using the confidence interval in part iii., can we infer at the 5% significance level that the population mean floor exercise score in the Individual All-Around Finals is different for female gymnasts and male gymnastics?

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Chapter12: Angle Relationships And Transformations

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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 A: Individual All-Around Finals

We will first look at the floor exercise scores in the Individual Female All-Around Finals and in the Individual Male All-Around Finals.

Female All-Around Finals Floor Exercise	Male All-Around Finals Floor Exercise
15	13.55
14.85	13.75
15.2	13.5
14.25	14.25
13.85	13.35
13	13.85
13.6	13.5
13.7	13.1
14.05	12.8
12.7	12.35
14.05	13.25
13.65	10.6
13.25	12.6
13.25	13.35
13.55	13.5
12.95	13.55
13.55	12.9
13.05	11.8
11.85	13.05
13.2	13.4
11	12.05
13.8	11.05
12.25	11.8
12.1	11.8
12.1	11.9
11.6	12.35
11.9	12.5
12.05	12.35
10.75	11.95
11.2	12.05
10.55	11.6
11.1	10.9
10.45	12.5
9.6	12.05
13.85	13
14.25	13.6
14.8	13.8
14	12.55
14.5	12.8
13.75	12
13.55	13.5
12.55	12.05
13.2	13.15
13.7	13.25
13.35	11.8
13.25	12.75
12.95	12.35
13.4	12.75
13.35	12.2
13.3	12.85
12.3	12.45
13.55	12.7
12.8	12.55
12.4	12.35
13.1	12.25
12.3	12.45
12.6	13
12.65	12.05
11.9	12
10.2	12.5
12.05	12.2
11.7	12.25
10.4	11.85
10.75	11.95
9.8	11.5
9.6	11.5
10.75	9.7
9.75	10.55
9.55	10
9.05	12.1
14.65	12.85
14.2	12.65
15.35	12.9
14.6	11.8
14.3	12.9
14.75	12.45
13.65	11.95
13.7	12.1
14.25	11.8
13.8	12.35
14.1	12.1
13.6	12
14	11.85
14.25	12.2
13.2	11.7
14.4	12.15
13.25	11.3
13.7	11.3
13.15	12.4
13.05	12
13.45	12
12.4	11.45
13.3	11
12.75	10.85
12.2	11.25
12.6	10.6
11.55	10.5
11.6	10.1
11.6	11
10	11
10.9	10.85
10.35	10.35
11.75	10.2
11.3	11.05
10.3
10.9

i. Find the sample mean and sample standard deviation for the floor exercise scores in the Individual Female All-Around Finals.

ii. Find the sample mean and sample standard deviation for the floor exercise scores in the Individual Male All-Around Finals.

iii. Construct a 95% confidence interval for the difference in population mean floor exercise scores between female and male gymnasts in the Individual All-Around Finals. (Hint: Use the results of i. and ii. and use the t-distribution.)

iv. Using the confidence interval in part iii., can we infer at the 5% significance level that the population mean floor exercise score in the Individual All-Around Finals is different for female gymnasts and male gymnastics?

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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