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Spectators are interested to know if the ages of gymnasts competing in the Canada Games are uniformly distributed. To investigate this hypothesis, we will consider the female gymnasts and male gymnasts who competed in the 2015 Team Competition as a sample of all Canada Games gymnasts.   Female Gymnasts Age Male Gymnasts Age 15 17 16 12 17 17 14 15 16 16 15 16 17 12 14 14 16 17 18 13 13 18 14 14 16 18 14 19 11 17 17 17 14 17 14 14 14 18 12 17 16 18 16 17 14 18 14 17 16 18 16 18 18 15 16 14 13 16 16 18 16 14 17 16 16 16 17 18 17 17 18 14 13 11 16 18 12 17 11 17 18 16 16 14 13 14 15 13 15 13 17 14 15 11 14 13 17 18 18 18 14 13 14 18 15 16 14 15 14 14 11 13 13 14 16 16 13 15 14   a) Construct a single histogram of the ages of all male and female gymnasts. What do you notice about the distribution of ages? Provide a possible explanation for what you observe. b) Should we reject or not reject the claim that the distribution of gymnasts’ ages is uniform at the 5% significance level? (Hint: Apply the ?2 test of goodness of fit.) Remember to state the hypothesis, state the formula, and show all steps in calculations. (Hint: Don't forget the ?2 critcal value.)

Spectators are interested to know if the ages of gymnasts competing in the Canada Games are uniformly distributed. To investigate this hypothesis, we will consider the female gymnasts and male gymnasts who competed in the 2015 Team Competition as a sample of all Canada Games gymnasts.   Female Gymnasts Age Male Gymnasts Age 15 17 16 12 17 17 14 15 16 16 15 16 17 12 14 14 16 17 18 13 13 18 14 14 16 18 14 19 11 17 17 17 14 17 14 14 14 18 12 17 16 18 16 17 14 18 14 17 16 18 16 18 18 15 16 14 13 16 16 18 16 14 17 16 16 16 17 18 17 17 18 14 13 11 16 18 12 17 11 17 18 16 16 14 13 14 15 13 15 13 17 14 15 11 14 13 17 18 18 18 14 13 14 18 15 16 14 15 14 14 11 13 13 14 16 16 13 15 14   a) Construct a single histogram of the ages of all male and female gymnasts. What do you notice about the distribution of ages? Provide a possible explanation for what you observe. b) Should we reject or not reject the claim that the distribution of gymnasts’ ages is uniform at the 5% significance level? (Hint: Apply the ?2 test of goodness of fit.) Remember to state the hypothesis, state the formula, and show all steps in calculations. (Hint: Don't forget the ?2 critcal value.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Spectators are interested to know if the ages of gymnasts competing in the Canada Games are uniformly distributed. To investigate this hypothesis, we will consider the female gymnasts and male gymnasts who competed in the 2015 Team Competition as a sample of all Canada Games gymnasts.  

Female Gymnasts Age Male Gymnasts Age
15 17
16 12
17 17
14 15
16 16
15 16
17 12
14 14
16 17
18 13
13 18
14 14
16 18
14 19
11 17
17 17
14 17
14 14
14 18
12 17
16 18
16 17
14 18
14 17
16 18
16 18
18 15
16 14
13 16
16 18
16 14
17 16
16 16
17 18
17 17
18 14
13 11
16 18
12 17
11 17
18 16
16 14
13 14
15 13
15 13
17 14
15 11
14 13
17 18
18 18
14 13
14 18
15 16
14 15
14 14
11 13
13 14
16 16
13 15
14  

a) Construct a single histogram of the ages of all male and female gymnasts. What do you notice about the distribution of ages? Provide a possible explanation for what you observe.

b) Should we reject or not reject the claim that the distribution of gymnasts’ ages is uniform at the 5% significance level? (Hint: Apply the ?2 test of goodness of fit.) Remember to state the hypothesis, state the formula, and show all steps in calculations. (Hint: Don't forget the ?2 critcal value.) 

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