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.

TIME SPENT STUDYING	A	B	C
LESS THAN 3 HOURS	4	19	8
3-5 HOURS	18	17	5
MORE THAN 5 HOURS	16	13	4

a. Using APLHA = 0.01 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. Upper H 0 ​: Grade and time spent studying are independent of one another. Upper H 1 ​: Grade and time spent studying are not independent of one another.

B. Upper H 0 ​: Grade and time spent studying are not independent of one another. Upper H 1 ​: Grade and time spent studying are independent of one another.

C. Upper H 0 ​: The variables​ A, B,​ C, less than 3​ hours, 3dash 5 ​hours, and more than 5 hours are independent. Upper H 1 ​: At least one of the variables is not independent.

D. Upper H 0 ​: The variables​ A, B,​ C, less than 3​ hours, 3dash 5 ​hours, and more than 5 hours are independent. Upper H 1 ​: None of the variables are independent.

Find the​ chi-square test statistic.

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

Determine the​ p-value. ​

= ​____________________(Round to three decimal places as​needed.)

Determine the result of the test.

The​ p-value is: ▼ greater than less than alpha equals 0.01​, so ▼ reject do not reject Upper H 0 . b. What conclusions can be made based on these​ results? There is ▼ insufficient sufficient evidence to indicate that ▼

Answer 1

The statistical software output for this problem is:

Hence,

Hypotheses: Option A is correct.

Test statistic = 11.15

P - value = 0.0249

Results: Greater than; Do not Reject; Insufficient; Grade and time spent studying are not independent of one another.