Question

"You are interested in determining whether there is a relationship between the grade level of students at Big Rock School District and their primary color preference for a new school football uniform. A sample of students (grades 8, 9, 12) is asked which color (black, blue, gold) they would prefer for a new school football uniform. Assuming the .05 level of significance, what would you conclude?" 8th grade mean 13.0, 9th grade mean: 12.6, 12th grade mean: 8.0.

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. No Data on 6 and 8 grades given on data sheeet

Answer 1

The provided data is the categorical variable

If the variable is continuous then for identity relationship between two variable we use correlation.

If the variable is categorical then for identity relationship between two variable we use chi-square test.

here variables are categorical so we used chi-square.

Test of Hypothesis:

H0: The choice of colors does not depend on the grade of students.

against,

H1: The choice of colors is depending on the grade of students.

Test Statistics,

Chi-square = sum( [ (O - E)² / E ] )

Decision Rule:

If the p-value is greater than the level of significance 0.05 (5%) then accept the null hypothesis.

R Output:

> grades = c(8,9,12)

> color = c('black','blue','gold')

> chisq.test(grades,color)

Pearson's Chi-squared test

data: grades and color

X-squared = 6, df = 4, p-value = 0.1991

The p-value is 0.1991 > 0.05 at 5% level of significance.

So accept the null hypothesis.

i.e. The choice of colors does not depend on the grade of students.

>>>>>>>>>>>>>> Best Luck >>>>>>>>>>>>>>>