Question

4. Of 150 students, 85 had a sibling and graduated, 20 had a sibling but did not graduate, 35 had no siblings and graduated, and 10 had no siblings and did not graduate.

What is E for sibling and graduated?

What is chi-squared for the above example?

What is the critical chi-square value if alpha=.01?

Based on the above, you would __________ Ho and conclude that sibling and graduation status are ____________.

Answer 1

The provided data can be interpreted as,.

	Sibling	No Sibling	Total
Graduated	85	35	120
Not Graduated	20	10	30
Total	105	45	150

In the above table, total rows (r) is 2 and the total columns (c) is 2.

The statistical hypothesis is:

Ho: There is no relationship between the sibling and graduation status.

Ha: There is a relationship between the sibling and graduation status.

The formula to calculate expected counts is given by,

The expected counts (Ei) calculation is shown in the below table:

	Sibling	No Sibling	Total
Graduated	E1 = (120 x 105)/150 = 84	E2 = (120 x 45)/150 = 36	120
Not Graduated	E3 = (30 x 105)/150 = 21	E4 = (30 x 45)/150 = 9	30
Total	105	45	150

The test statistic can be calculated as:

Therefore, the test statistic is 0.198.

The degrees of freedom (v) is,

The critical value obtained at the 0.01 significance levl and the degrees of freedom 1 from the chi-square table is 6.6349.

Thus, the test statistic (0.198) is less than the critical value (6.6349), so the researcher rejects the null hypothesis.

(i): The expected value E for sibling and graduated is 84.

(ii): The chi-squared value is 0.198.

(iii): The critical chi-square value if alpha=.01 is 6.6349.

(iv): Based on the above, you would fail to reject Ho and conclude that sibling and graduation status are independent; that is, there is no relationship between the sibling and graduation status.