Question

Refer to the following contingency chart comparing 3 college programs (criminal justice, business, culinary) with the GPA of students graduating from those programs at a college.

                                            2.0-2.5            2.5-3.0            3.0-3.5               3.5-4.0

criminal justice                     23                    18                     32                       47

business                               17                     26                    36                        31

culinary                                 28                     17                    41                       28

A. What is the overall total number of students in this contingency table?

B. What is the observed value for business students with a GPA of 3.0-3.5?

C. What is the expected value for criminal justice students with a GPA of 2.0-2.5?

D. The total number of students with a GPA 2.5-3.0 is?

E. What is the total number of culinary students?

F. What is the value for (O-E)²/E value for the criminal justice students with a GPA of 2.0-2.5?

G. What is the value of the test statistic?

H. Assuming α = 2.5%, the critical value is ?

I. Assuming α = 2.5%, what is the conclusion to this independence test?

Answer 1

A. What is the overall total number of students in this contingency table?

345

B. What is the observed value for business students with a GPA of 3.0-3.5?

36

C. What is the expected value for criminal justice students with a GPA of 2.0-2.5?

23.6522

D. The total number of students with a GPA 2.5-3.0 is?

68

E. What is the total number of culinary students?

115

F. What is the value for (O-E)2/E value for the criminal justice students with a GPA of 2.0-2.5?

0.0180

G. What is the value of the test statistic?

11.1926

H. Assuming α = 2.5%, the critical value is ?

14.4494

I. Assuming α = 2.5%, what is the conclusion to this independence test?

DO NOT REJECT H0

Test performed:

Consider the following table. That will answer most of the questions:

Chi-Square Independence test - Results

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H0​: The two variables - College programs and GPA are independent Ha​: The two variables - College programs and GPA are dependent This corresponds to a Chi-Square test of independence. (2) Degrees of Freedom The number of degrees of freedom is df = (3 - 1) * (4 - 1) = 6 (3) Critical value and Rejection Region Based on the information provided, the significance level is α=0.025, the number of degrees of freedom is df = (3 - 1) * (4 - 1) = 6, so the critical value is 14.4494. Then the rejection region for this test becomes R={χ2:χ2>14.4494}. (4)Test Statistics The Chi-Squared statistic is computed as follows: (5)P-value The corresponding p-value for the test is p=Pr(χ2​>11.1926)=0.0826 (6)The decision about the null hypothesis Since it is observed that χ2=11.1926<χ2_c​rit=14.4494, it is then concluded that the null hypothesis is NOT rejected. (7)Conclusion It is concluded that the null hypothesis Ho is NOT rejected. Therefore, there is NOT enough evidence to claim that the two variables - College programs and GPA are dependent, at the 0.025 significance level. Conditions: a. The sampling method is simple random sampling. b. The data in the cells should be counts/frequencies c. The levels (or categories) of the variables are mutually exclusive.

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