Chapter 25, Problem 25.44E

a.

To determine

To test and conclude: Whether there is a relationship between the highest degrees obtained and attended religious services.

Answer to Problem 25.44E

There is sufficient evidence to support the claim that there is a relationship between the highest degrees obtained and attended religious services. That is, the attending religious service has effect on getting degrees.

Explanation of Solution

Given info:

The statement “Did any one attended religious services last week” was asked to randomly selected subjects.

Calculation:

The claim is to test whether there is any relationship between the highest degrees obtained and attended religious services.

Cell frequency for using Chi-square test:

When at most 20% of the cell frequencies are less than 5

If all the individual frequencies are 1 or more than 1.

All the expected frequencies must be 5 or greater than 5

The hypotheses used for testing are given below:

$H_0:$ There is no relationship between the highest degree obtained and attended religious services.

$H_a:$ There is relationship between the highest degree obtained and attended religious services.

Software procedure:

Software procedure for calculating the chi-square test statistic is given below:

Click on Stat, select Tables and then click on Chi-square Test (Two-way table in a worksheet).

Under Columns containing the table: enter the columns of High School, Junior College, Bachelor, and Graduate.

Click ok.

Output obtained from MINITAB is given below:

Thus, the test statistic is 14.190, the degree of freedom is 3 and the P-value is 0.003.

Since all the expected frequencies are greater than 5, the usage of chi-square test is appropriate.

Conclusion:

The P-value is 0.003 and level of significance is 0.05.

Thus, the P-value is lesser than the level of significance.

The null hypothesis is rejected.

Thus, there is sufficient evidence to support the claim that there is a relationship between the highest degrees obtained and attended religious services.

b.

To determine

To make: A $2\times 3$ two way table when omitting the column “High School”.

To test: Whether there is relationship between the types of highest degrees obtained and attended religious services and describes the result.

Answer to Problem 25.44E

The $2\times 3$ two way table after leaving the column “High School” is given below:

	Highest degree obtained
Attended Services	Junior College	Bachelor	Graduate
Yes	62	146	76
No	101	232	105

There is no sufficient evidence to support the claim that there is relationship between the types of highest degrees obtained and attended religious services.

The relationship between the types of highest degrees obtained and attended religious services changes.

Explanation of Solution

Calculation:

The claim is to test whether there is any relationship between the types of highest degrees obtained and attended religious services.

The hypotheses used for testing are given below:

$H_0:$ There is no relationship between the types of highest degrees obtained and attended religious services.

$H_a:$ There is relationship between the types of highest degrees obtained and attended religious services.

Software procedure:

Software procedure for calculating the chi-square test statistic is given below:

• Click on Stat, select Tables and then click on Chi-square Test (Two-way table in a worksheet).
• Under Columns containing the table: enter the columns of Junior College, Bachelor, and Graduate.
• Click ok.

Output obtained from MINITAB is given below:

Thus, the test statistic is 0.729, the degree of freedom is 2 and the P-value is 0.694.

Since all the expected frequencies are greater than 5, the usage of chi-square test is appropriate.

Conclusion:

The P-value is 0.694 and level of significance is 0.05

Thus, the P-value is greater than the level of significance.

The null hypothesis is not rejected.

Thus, there is no sufficient evidence to support the claim that there is relationship between the types of highest degrees obtained and attended religious services.

When the High school degree column is omitted, the relationship between the types of highest degrees obtained and attended religious services do not exist.

c.

To determine

To make: A $2\times 2$ two way table by adding the columns of “Junior School”, “Bachelor” and “Graduate”.

To test: Whether there is relationship between getting a degree beyond high school and attended religious services.

Answer to Problem 25.44E

The $2\times 2$ two way table is given below:

	Highest Degree obtained
Attended Services	High School	Degrees beyond High School
Yes	62	284
No	101	438

There is not sufficient evidence to support the claim that there is relationship between getting a degree beyond high school and attended religious services

There is no influence of attending religious services on getting highest degree hold.

Explanation of Solution

Calculation:

A two way table by adding the columns of “Junior School”, “Bachelor” and “Graduate” is given below:

	Highest Degree obtained
Attended Services	Junior College	Bachelor	Graduate	Total
Yes	62	146	76	284
No	101	232	105	438

Thus, combining the total obtained from the above table and the column of “High school”. The $2\times 2$ two way table can be obtained as follows:

	Highest Degree obtained
Attended Services	High School	Degrees beyond High School
Yes	62	284
No	101	438

The claim is to test whether there is any relationship between getting a degree beyond high school and attended religious services.

The hypotheses used for testing are given below:

$H_0:$ There is no relationship between getting a degree beyond high school and attended religious services.

$H_a:$ There is relationship between getting a degree beyond high school and attended religious services.

Software procedure:

Step by step procedure for calculating the chi-square test statistic using MINITAB software.

• Click on Stat, select Tables and then click on Chi-square Test (Two-way table in a worksheet).
• Under Columns containing the table: enter the columns of High School and Degree beyond high school.
• Click ok.

Output obtained from MINITAB is given below:

Thus, the test statistic is 0.094, the degree of freedom is 1 and the P-value is 0.759.

Since all the expected frequencies are greater than 5, the usage of chi-square test is appropriate.

Conclusion:

The P-value is 0.759 and level of significance is 0.05

Thus, the P-value is greater than the level of significance.

The null hypothesis is not rejected.

Thus, there is no sufficient evidence to support the claim that there is a relationship between getting a degree beyond high school and attended religious services.

d.

To determine

To explain: The relationship between the highest degree obtained and attending religious services in part (a), (b) and (c).

To find: The percentage who attended religious services across each category of highest degree obtained.

Answer to Problem 25.44E

The relationship between the highest degree obtained and attending religious services depends on the individuals or the samples because High school people have higher percentage in attending religious service.

After omitting the “High School” column, the analysis shows no relationship between the highest degree obtained and attending religious services.

The percentage who attended religious services across each category of highest degree is given below:

Highest Degree Hold	Percentage of Attended services
High School	58.5%
Junior College	9.1%
Bachelor	21.3%
Graduate	11.1%

Explanation of Solution

From the analysis obtained in part (a), there is a relationship between the attended religious services and highest degree.

From the analysis obtained in part (b), there is no relationship between the attended religious services and highest degree because the column “High school” is left out from the analysis.

From the analysis obtained in part (c), there is no relationship between the attended religious services and highest degree because the columns of “Junior School”, “Bachelor” and “Graduate” and the analysis was carried out.

The above result shows that the highest degree is affected by attending religious services.

Calculation:

The percentage who attended religious services across each category of highest degree is calculated below:

Highest Degree Hold	Percentage of Attended services
High School	$\begin{array}{c}\frac{400}{684}\times 100=0.585\times 100\\ =58.5\end{array}$
Junior College	$\begin{array}{c}\frac{62}{684}\times 100=0.091\times 100\\ =9.1\end{array}$
Bachelor	$\begin{array}{c}\frac{146}{684}\times 100=0.213\times 100\\ =21.3\end{array}$
Graduate	$\begin{array}{c}\frac{76}{684}\times 100=0.111\times 100\\ =11.1\end{array}$