Chi-Square Test

To determine if selected variable is related to the choice of TEP type, the Chi-Square test of independence is conducted as below:

A) Family Income

Table 1: TEPtype * Family Income Crosstabulation

Family Income

Total1.0 2.0 3.0 4.0 5.0

TEPtype Public University Count 81 41 16 2 0 140

Expected Count 68.6 41.3 23.8 5.6 .7 140.0

% within Family Income 82.7% 69.5% 47.1% 25.0% 0.0% 70.0%

Private University Count 17 18 18 6 1 60

Expected Count 29.4 17.7 10.2 2.4 .3 60.0

% within Family Income17.3% 30.5% 52.9% 75.0%

100.0

%30.0%

Total Count 98 59 34 8 1 200

Expected Count 98.0 59.0 34.0 8.0 1.0 200.0

% within Family Income 100.0

%

100.0

%

100.0

%

100.0

%

100.0

%

100.0

%

The null and alternative hypotheses of this test are:

Ho: “Family Income” variable is not related to the choice of TEP type.

Ha: “Family Income” variable is related to the choice of TEP type.

Ho is rejected if the p-value of the test statistic is smaller than α . Let α taken as 0.05.

Table 2: Chi-Square Tests

Value df

Asymp. Sig. (2-

sided)

Pearson Chi-Square 26.047a 4 .000

Likelihood Ratio 25.325 4 .000

Linear-by-Linear Association 25.316 1 .000

N of Valid Cases 200

a. 3 cells (30.0%) have expected count less than 5. The minimum

expected count is .30.

The Chi-Square tests results is shown in Table 2. The p-value of the Pearson Chi-Square is

0.000. Since it is smaller than α, we will reject the null hypotheses. Therefore, we have

enough evidence to conclude that “Family Income” variable is related to the choice of TEP

type and H1: Family level of income is significantly related to the student’s choice of college

is valid.

B) Good Result

Table 1.TEPtype * GoodResult Crosstabulation

GoodResult

Total1.0 2.0 3.0 5.0

TEPtype Public University Count 27 83 30 0 140

Expected Count 28.0 81.2 30.1 .7 140.0

% within GoodResult 67.5% 71.6% 69.8% 0.0% 70.0%

Private University Count 13 33 13 1 60

Expected Count 12.0 34.8 12.9 .3 60.0

% within GoodResult 32.5% 28.4% 30.2% 100.0% 30.0%

Total Count 40 116 43 1 200

Expected Count 40.0 116.0 43.0 1.0 200.0

% within GoodResult 100.0% 100.0% 100.0% 100.0% 100.0%

The null and alternative hypotheses of this test are:

Ho: “Good Result” variable is not related to the choice of TEP type.

Ha: “Good Result” variable is related to the choice of TEP type.

Ho is rejected if the p-value of the test statistic is smaller than α . Let α taken as 0.05.

Table 2. Chi-Square Tests

Value df

Asymp. Sig. (2-

sided)

Pearson Chi-Square 2.586a 3 .460

Likelihood Ratio 2.661 3 .447

Linear-by-Linear Association .074 1 .785

N of Valid Cases 200

a. 2 cells (25.0%) have expected count less than 5. The minimum

expected count is .30.

The Chi-Square tests results is shown in Table 2. The p-value of the Pearson Chi-Square is

0.460. Since it is bigger than α, we will reject Alternative hypotheses. Therefore, we have

enough evidence to conclude that “Good result” variable is not related to the choice of TEP

type and Ho: Good Result is not significantly related to the student’s choice of college is

valid.

C) Location

Table 1.TEPtype * Location Crosstabulation

Location

Total1.0 2.0 3.0

TEPtype Public University Count 43 83 14 140

Expected Count 44.1 75.6 20.3 140.0

% within Location 68.3% 76.9% 48.3% 70.0%

Private University Count 20 25 15 60

Expected Count 18.9 32.4 8.7 60.0

% within Location 31.7% 23.1% 51.7% 30.0%

Total Count 63 108 29 200

Expected Count 63.0 108.0 29.0 200.0

% within Location 100.0% 100.0% 100.0% 100.0%

The null and alternative hypotheses of this test are:

Ho: “Location” variable is not related to the choice of TEP type.

Ha: “Location” variable is related to the choice of TEP type.

Ho is rejected if the p-value of the test statistic is smaller than α . Let α taken as 0.05.

Table 2. Chi-Square Tests

Value df

Asymp. Sig. (2-

sided)

Pearson Chi-Square 9.023a 2 .011

Likelihood Ratio 8.566 2 .014

Linear-by-Linear Association 1.486 1 .223

N of Valid Cases 200

a. 0 cells (0.0%) have expected count less than 5. The minimum

expected count is 8.70.

The Chi-Square tests results is shown in Table 2. The p-value of the Pearson Chi-Square is

9.023. Since it is bigger than α, we will reject Alternative hypotheses. Therefore, we have

enough evidence to conclude that “Location” variable is not related to the choice of TEP type

and Ho: Location is not significantly related to the student’s choice of college is valid.

D) Cost

Table 1.TEPtype * Cost Crosstabulation

Cost

Total1.0 2.0 3.0 4.0

TEPtype Public University Count 84 32 21 3 140

Expected Count 70.0 37.1 25.2 7.7 140.0

% within Cost 84.0% 60.4% 58.3% 27.3% 70.0%

Private University Count 16 21 15 8 60

Expected Count 30.0 15.9 10.8 3.3 60.0

% within Cost 16.0% 39.6% 41.7% 72.7% 30.0%

Total Count 100 53 36 11 200

Expected Count 100.0 53.0 36.0 11.0 200.0

% within Cost 100.0% 100.0% 100.0% 100.0% 100.0%

The null and alternative hypotheses of this test are:

Ho: “Cost” variable is not related to the choice of TEP type.

Ha: “Cost” variable is related to the choice of TEP type.

Ho is rejected if the p-value of the test statistic is smaller than α . Let α taken as 0.05.

Table 2. Chi-Square Tests

Value df

Asymp. Sig. (2-

sided)

Pearson Chi-Square 23.566a 3 .000

Likelihood Ratio 23.445 3 .000

Linear-by-Linear Association 21.085 1 .000

N of Valid Cases 200

a. 1 cells (12.5%) have expected count less than 5. The minimum

expected count is 3.30.

The Chi-Square tests results is shown in Table 2. The p-value of the Pearson Chi-Square is

23.566. Since it is bigger than α, we will reject Alternative hypotheses. Therefore, we have

enough evidence to conclude that “Cost” variable is not related to the choice of TEP type and

Ho: Cost is not significantly related to the student’s choice of college is valid.