Question

The following contingency table shows the distribution of grades earned by students taking a midterm exam in an MBA​ class, categorized by the number of hours the students spent studying for the exam. Complete parts a. and b. below.

Click the icon to view the contingency table.

Grade

Time spent Studying    A B    C

Less than 3 hours    3 18    11

3-5 hours 16 13    7

More than 5 hours 23 14    4

a. Using α=0.05​, perform a​ chi-square test to determine if a​ student's grade on the exam and the hours spent studying for it are independent of one another.

Identify the null and alternative hypotheses for a​ chi-square test of independence based on the information in the table. Choose the correct answer below.

A. H0​: Grade and time spent studying are not independent of one another. H1​: Grade and time spent studying are independent of one another.

B. H0​: Grade and time spent studying are independent of one another. H1​: Grade and time spent studying are not independent of one another.

C. H0​: The variables​ A, B,​ C, less than 3​ hours, 3 –5 ​hours, and more than 5 hours are independent. H1​: At least one of the variables is not independent.

D. H0​: The variables​ A, B,​ C, less than 3​ hours, 3–5 ​hours, and more than 5 hours are independent. H1​: None of the variables are independent.

Find the​ chi-square test statistic.

χ2= ​(Round to two decimal places as​ needed.)

Determine the​ p-value. ​

p-value = ​(Round to three decimal places as​ needed.)

Determine the result of the test. The​ p-value is (greater than/less than) α= 0.05​, so (reject/do not reject) H0.

b. What conclusions can be made based on these​ results? There is (insufficient/sufficient) evidence to indicate that (grade and time spent studying are not independent of one another/none of the variables are independent//at least one of the variables is not independent///grade and time spent studying are independent of one another.)

Answer 1

B. H0​: Grade and time spent studying are independent of one another. H1​: Grade and time spent studying are not independent of one another.

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	A	B	C	Total
	<3 hours	12.3303	13.2110	6.4587	32.00
	3-5 hours	13.8716	14.8624	7.2661	36.00
	>5 hours	15.7982	16.9266	8.2752	41.00
	total	42.00	45.00	22.00	109.00
chi square    χ2	=(Oi-Ei)2/Ei	A	B	C	Total
	<3 hours	7.060	1.736	3.193	11.9893
	3-5 hours	0.327	0.233	0.010	0.5697
	>5 hours	3.283	0.506	2.209	5.9978
	total	10.6698	2.4754	5.4115	18.557
test statistic X2 =	18.56

p value =0.001

b)

There is sufficient evidence to indicate that grade and time spent studying are not independent of one anothe