Question

The number of students in one of the small towns reached (2000) male and female students, who move to their schools by means, as in the following table:

	Walking	Private Transportation	School Transportation	TOTAL
Male	340	590	120	1050
Female	260	560	130	960
TOTAL	600	1150	250	2000

Study the relationship between the type of pupils and the mode of transportation, and answer the following questions:

A - Formulate the appropriate null hypothesis.

B - Determine the value of the appropriate level of significance.

C - Set the degrees of freedom.

D - Calculate the value of a square of X2.

E - Extract the critical X² value from the table. And - test your zero hypothesis, and make the appropriate decision about it, and what does it mean?

Answer 1

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H0​: The two variables - the type of pupils and the mode of transportation are independent Ha​: The two variables - the type of pupils and the mode of transportation are dependent This corresponds to a Chi-Square test of independence. (2) Since the level of significance is not provided, assuming it to be 5%. (3)Degrees of Freedom The number of degrees of freedom is df = (2 - 1) * (3 - 1) = 2 (4)Test Statistics The Chi-Squared statistic is computed as follows: (5) Critical value and Rejection Region Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df = (2 - 1) * (3 - 1) = 2, so the critical value is 5.9915. Then the rejection region for this test becomes R={χ2:χ2>5.9915}. P-value The corresponding p-value for the test is p=Pr(χ2​>6.8664)=0.0323 The decision about the null hypothesis Since it is observed that χ2=6.8664>χ2_c​rit=5.9915, it is then concluded that the null hypothesis is rejected. Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables are dependent, at the 0.05 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.