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Resistance training is a popular form of conditioning aimed at enhancing sport performance and is widely...

Resistance training is a popular form of conditioning aimed at enhancing sport performance and is widely used among high school, college, and professional athletes. A random sample of 285 patients of three age groups admitted to the emergency rooms with the injury code "weightlifting" was obtained. These injuries were classified as accidental if caused by dropped weight or improper equipment use. Is age and sport injury related? (PLEASE WRITE CLEARLY AND AS SIMPLE AS POSSIBLE)

Chi - Square X2 Test for independence (two-way test) or  Chi - Square X 2 Goodness of Fit (Expected vs, Observed) or is there another way that I am missing??

Age Group - Accidental - Not Accidental - Total

Adolescents: 35 - 15 - 50

Young Adults: 60 - 95 - 155

Older Adults: 20 - 60 - 80

Totals: 115 - 170 - 285

A: Set up the Hypothesis testing Ho and H1 for chi square

B. Use Chi Square formula and Procedure to solve the problem

C. Discuss the results. What do the results tell us? is there a significant relationship between age and injury?

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Answer #1

This is chi-square test of independence

a)

Ho : Age and Sport Injury are independent

Ha : Age and Sport Injury are dependent

b)

The following cross tablulation have been provided. The row and column total have been calculated and they are shown below Row 1 Row 2 Row 3 Total Column1 35 60 20 115 Column 2 15 95 60 170 Total 50 155 80 285 The expected values are computed in terms of row and column totals. In fact, the formula is Ei where Ri corresponds to the total sum of elements in row i, Cj corresponds to the total sum of elements in column j, and T is the grand total. The table below shows the calculations to obtain the table with expected values Expected Values Column1 115*50/285 20.175 115 155/285 - Column 2 170 50/285 29.825 170*155/285 = Total Row 1 50 Row 2 155 62.544 115*80/285 = 32.281 115 92.456 170 80/285 -47.719 170 Row 3 80 Total 285 Based on the observed and expected values, the squared distances can be computed according to the following formula: (E - O)2/E. The table with squared distances is shown below. Expected Values Column1 115*50/285 20.175 115 155/285 - Column 2 170 50/285 29.825 170155/285 - Total Row 1 50 Row 2 155 62.544 115*80/285 32.281 115 92.456 170 80/285 -47.719 170 Row 3 80 Total 285

Based on the information provided, the significance level is a 0.05, the number of degrees of freedom is df (3-1) x (2-1-2, so then the rejection region for this test is R :>5.991) The Chi-Squared statistic is computed as follows: x2ー w 10.893 0.103 + 4.672+ 7.3694 0.07 + 3.16-26.267 Bij Since it is observed that x rejected 26.2672 5.991, it is then concluded that the null hypothesis is t is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables are dependent, at the 0.05 significance level

c)

There is a significant relationship between age and injury

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