Question

In: Statistics and Probability

Students in a high school were asked whether good grades, athletic ability, or popularity was most...

Students in a high school were asked whether good grades, athletic ability, or popularity was most important to them. A two-way table separating the students by gender and by choice of most important factor (factor) is shown below:

	Boys	Girls
Grades	12	16
Popularity	16	32
Sports	30	14
			100

For the data above, do the following

Calculate the row and column totals
Calculate gender by factor percentages
Calculate factor by gender percentages
What is the test to be done to determine whether is an association between gender and factor?
What are the degrees of freedom for that test (show formula and calculation)
Create a table of expected frequencies
Create a table of c² values (calculate c²for each cell)
What is the total calculated c²?
From the chi-square table (https://www.medcalc.org/manual/chi-square-table.php) find the critical value of chi-square for the degrees of freedom in part e. of this question and for an alpha value of .05.
Compare the calculated and critical value of chi-square, what is your inference (state your null and alternate hypothesis and draw your inference.

Expert Solution

a)

	Boys	Girls	Total
Grades	12	16	28
Popularity	16	32	48
Sports	30	14	44
Total	58	62	120

b)

Gender by factor percentages
	Boys	Girls	Total
Grades	42.85714%	57.14286%	100%
Popularity	33.33333%	66.66667%	100%
Sports	68.18182%	31.81818%	100%

c)

Factor by gender percentages
	Boys	Girls
Grades	20.68966%	25.80645%
Popularity	27.58621%	51.6129%
Sports	51.72414%	22.58065%
Total	100%	100%

d)

Chi square test of independence need to be done to test the association between gender and factor

e)

Where, r is the number of rows and c is the number of column in the table.

f)

The expected values are obtained using the formula,

	Boys	Girls	Total
Grades			28
Popularity			48
Sports			44
Total	58	62	120

g)

The Chi-Square Value is obtained using the formula

Observed,	Expected,
12	13.53333333	-1.533	2.351	0.174
16	23.2	-7.200	51.840	2.234
30	21.26666667	8.733	76.271	3.586
16	14.46666667	1.533	2.351	0.163
32	24.8	7.200	51.840	2.090
14	22.73333333	-8.733	76.271	3.355
				11.603

h)

i)

From the chi square table,

For significance level = 0.05 and degree of freedom = 2, the critical value is,

j)

Since the chi square value is greater than the critical value, It can be concluded that the null hypothesis is rejected at 5% significance level.

Hence both the variables factor and gender are dependent.

orchestra answered 1 year ago

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