QUESTION 2 \"You are interested in determining whether there is a relationship b
ID: 3049724 • Letter: Q
Question
QUESTION 2 "You are interested in determining whether there is a relationship between the grade level of students at Big uniform. Assuming the.05 level of significance, what would you conclude?" Rock School District and their primary color preference for a new school football uniform. A sample of students (grades 7, 8, 9) is asked which color (black, blue, gold) they would prefer for a new school football There is no relationship between grade level and color preference for a new football uniform. There is a weak relationship between grade level and color preference for a new football uniform There is a moderate relationship between grade level and color preference for a new football uniform. There is a strong relationship between grade level and color preference for a new football uniform Untitled Edited Regular 11 B I L black blue gold 7th 19 8th 14 18 9th 10 18 10 23Explanation / Answer
We can do a Chi- square test to know that if color preference for a new school football uniform and grade level of students at the school.
Here,
Observed Statistic table
Expected statistics Table
Chi - square table
X2 = (E- O)2/E
here as dF = ( 3- 1) * (3-1) = 4
alpha = 0.05
X2 (Critical) = 9.4877
so here X2 > X2 (Critical) so we can say that there
Here as now we get the chi-square statistic, we can get Cramer's V as it is 3 X 3 contigency table
V = sqrt [(X2/n)/ min (k-1,r-1)] = sqrt [(15.16/127)/2] = 0.2443 which is in the range of 0.2 to 0.4 so it is in the range of moderate association between the variables.
0.1 or less - weak association
0.2 to 0.4 - moderate association
0.5 and more - strong association.
Here p - value = 0.0044 so here it is less than 0.01, so we can say that there is a strong relationship between grade level and color preference for a new footbal uniform. Option D is correct here.
7th 8th 9th Total black 19 14 10 43 blue 8 18 18 44 gold 23 7 10 40 Total 50 39 38 127