Question

A random sample of students of a university were classified according to the college in which they were enrolled and also according to whether they graduated from a high school in the state or out the state. The results are shown in the contingency table. At 0.05 level of significance, test if there is an association between college and high school in/out of state.

	Engineering	Arts and Science	Business	Other	Total
In State	16	14	13	13	56
Out of State	14	6	10	8	38
Total	30	20	23	21	94

State the hypotheses.

H0: The proportion of in-state high school equals the proportion of out-of-state high school; Ha: The proportion of in-state high school differs from the proportion of out-of-state high school.

H0: There is an association between college and high school in/out of state; Ha: There is no association between college and high school in/out of state.

H0: Collage and high school in/out of state are dependent; Ha: College and high school in/out of state are independent.

H0: There is no association between college and high school in/out of state; Ha: There is an association between college and high school in/out of state.

Continue to consider Question #6.

Fill in the expected counts in the table. Round to the first decimal place. Avoid any blank space. Partial credit is given.

	Engineering	Arts and Science	Business	Other	Total
In State					56
Out of State					38
Total	30	20	23	21	94

Continue to consider Question #6.

Find the value of test statistic using the rounded expected counts found in Question #7.

0.63

1.55

1.67

0.20

Continue to consider Question #6.

Find the rejection region.

X² > 12.592

X² > 15.507

X² > 9.488

X² > 7.815

Continue to consider Question #6.

What’s your conclusion at 0.05 level of significance?

Do not reject H0. Insufficient evidence that the proportion of in-state high school differs from the proportion of out-of-state high school.

Reject H0. Sufficient evidence that college and high school in/out of state are dependent.

Do not reject H0. Insufficient evidence of an association between college and high school in/out of state.

Do not reject H0. Insufficient evidence that college and high school in/out of state are independent.

Continue to consider Question #6.

Is the sample size large enough to perform this hypothesis test?

Yes, because all expected counts are at least 5.

No, because some expected and observed counts are below 10.

Yes, because all observed counts are at least 5.

Yes, because the total sample size is greater than 30.

Answer 1

5)

H0: There is no association between college and high school in/out of state; Ha: There is an association between college and high school in/out of state.

6)

Expected	Ei=row total*column total/grand total	Engineering	Arts and Science	Business	Other	Total
	in state	17.9	11.9	13.7	12.5	56.00
	out of state	12.1	8.1	9.3	8.5	38.00
	total	30.00	20.00	23.00	21.00	94.00

7)

Applying chi square test of independence:

test statistic X2 =

1.55

8)

  rejection region:

X² > 7.815

9)

Do not reject H0. Insufficient evidence that the proportion of in-state high school differs from the proportion of out-of-state high school.

Yes, because all expected counts are at least 5.