Question

on the excel

Annual Income	No H.S Degree	H.S Degree	Some College	Total
Low	65	45	35	145
Medium	43	66	52	161
High	34	35	52	121
Total	142	146	139	427

1) state the null hypothesis for this study.

2) check whether all chi-square assumptions are met

3) calculate chi-square test statistics for the hypothetical data shown above.

(1) calculate total column percentages.

(2) calculate expected frequencies for all cells.

(3) calculate chi-square for each cell using formula (Oi-Ei)2 Ei

(4) calculate chi-square statistic

4) Identify degree of freedom for the data

5) Identify critical value for the data

6) Calculate the P-value for the data

7) Draw a conclusion referring to test statistic and p-value

Answer 1

Solution:

Here, we have to use chi square test for independence of two categorical variables.

1) State the null hypothesis for this study.

Null hypothesis: H₀: The annual income and educational degree are independent from each other.

Alternative hypothesis: H_a: The annual income and educational degree are dependent.

We assume level of significance = α = 0.05

2) Check whether all chi-square assumptions are met

Required assumptions are given as below:

Given data is a categorical data.

Two variables should consist of two or more categorical and independent groups.

3) Calculate chi-square test statistics for the hypothetical data shown above.

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

E = row total * column total / Grand total

We are given

Number of rows = r = 3

Number of columns = c = 3

Degrees of freedom = df = (r – 1)*(c – 1) = 2*2 = 4

α = 0.05

Critical value = 9.487729037

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Column variable
Row variable	No Degree	Degree	Some college	Total
Low	65	45	35	145
Medium	43	66	52	161
High	34	35	52	121
Total	142	146	139	427

Expected Frequencies
	Column variable
Row variable	No Degree	Degree	Some college	Total
Low	48.22014052	49.578454	47.20140515	145
Medium	53.54098361	55.04918	52.40983607	161
High	40.23887588	41.372365	39.38875878	121
Total	142	146	139	427

Calculations
(O - E)
16.77986	-4.57845	-12.2014
-10.541	10.95082	-0.40984
-6.23888	-6.37237	12.61124

(O - E)^2/E
5.83913	0.42281	3.154022
2.075276	2.178424	0.003205
0.967313	0.981502	4.037787

Test statistic = Chi square = ∑[(O – E)^2/E] = 19.65946815

P-value = 0.000582933

(By using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the annual income and educational degree are dependent.