In order to assess the risk of impaired neurocognitive performance due to repeat

Question

In order to assess the risk of impaired neurocognitive performance due to repeated concussive events, investigators interviewed 91 randomly selected soccer athletes, 97 randomly selected non-soccer athletes, and 60 randomly selected non-athletes. This last group served as the control group. The main interest for the investigative team was whether there was compelling evidence for the existence of chronic neuropsychological dysfunction in the population of collegiate soccer players. Of interest here is whether or not the rates for concussive events are distributed evenly for soccer athletes, non-soccer athletes, and the controls. Table 1 provides cross-tabulated results for this study. Let = 0.05.
Note: To calculate the chi squared bits, plug in the observed counts as you see them and plug in the ROUNDED (to two decimal places) expected counts into the chi squared bits equation.

A) Fill in the expected frequencies and corresponding 2 contribution for each cell. Round all expected frequencies to 2 decimal places and all 2 contributions to 4 decimal places.
B) The appropriate null/alternative pair for this setting is:

Ho:The proportion of concussive events is distributed normally with a mean of 0 across sport participation category
Ha: The proportion of concussive events is not distributed normally with a mean of 0 across sport participation category

Ho:The proportion of concussive events is not distributed normally with a mean of 0 across sport participation category
Ha: The proportion of concussive events is distributed normally with a mean of 0 across sport participation category

     Ho: The proportion of concussive events is associated with sport participation category
Ha: The proportion of concussive events is not associated with sport participation category

Ho:The proportion of concussive events is distributed normally across sport participation category
Ha: The proportion of concussive events is not distributed normally across sport participation status

Ho: The proportion of concussive events is not associated with sport participation category
Ha: The proportion of concussive events is associated with sport participation category

C) The number of degrees of freedom for this study is:
D) The critical value is:
E) The test statistic is:
F) The proper conclusion for this test is:

FTR Ho and do not conclude that there is an association between the proportion of concussive events and the sport participation categories?

Reject Ho and conclude that there is no association between the proportion of concussive events and the sport participation categories?    Reject Ho and conclude that there is an association between the proportion of concussive events and the sport participation categories?

FTR Ho and do not conclude that there is no association between the proportion of concussive events and the sport participation categories?

Table 1: Cross-tab results for number of concussions by athlete type Number of Concussions Athlete Type 0 1 2 3 or more Total Soccer 48
Exp11 =?
211 = ? 24
Exp12 = ?
212 =? 12
Exp13 =?
213 = ? 7
Exp14 =?
214 = ? 91 Non-Soccer 66
Exp21 = ?
221 = ? 16
Exp22 = ?
222 = ? 10
Exp23 = ?
223 = ? 5
Exp24 = ?
224 = ? 97 Non-Athlete 50
Exp31 = ?
231 = ? 5
Exp32 =?
232 = ? 4
Exp33 =?
233 = ? 1
Exp34 =?
234 = ? 60 Total 164 45 26 13 248

Explanation / Answer

A) The expected frequenices are calculated as follows

B) correct Answer: Option (E)

Ho: The proportion of concussive events is not associated with sport participation category
Ha: The proportion of concussive events is associated with sport participation category

C)

Degrees of freedom: (3-1)(4-1) = 2*3 = 6

D)

Critical X^2: 12.59157

E)

Chisquare contribution values are

Test Statistic, X^2: 15.9058

F) Here Chisquare value > Chisquare critical value, we reject H0

Thus we conclude that the proportion of concussive events is associated with sport participation category

Correct Option: Reject Ho and conclude that there is an association between the proportion of concussive events and the sport participation categories

0 1 2 3 ormore Total Soccer 60.177 16.512 9.54 4.770161 90.99916 Non Soccer 64.145 17.601 10.169 5.085 97 Non Athlete 39.677 10.887 6.29 3.145161 59.99916 Total 163.999 45 25.999 13.00032 247.9983

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