Question

A random sample of 303 individuals collected the following information: sex, marital status, age, country, size, and type. The variables marital status and type (which refers to type of automobile—either family, sporty, or work) are of interest to us. We would like to know if there is a relationship between the two qualitative variables marital status and type. We will test our hypothesis at the α = 0.01 level of significance. The data is in the Excel file Car Poll.xlsx.

LINK TO DATA: should be able to view and edit

https://docs.google.com/spreadsheets/d/14PFhkZTV1p1i-kj5qOJ1ynhfD-GVkQFqlwZj-pwJ1zo/edit?usp=sharing

1. State the hypotheses of interest.
2. How many degrees of freedom will the test have? What is the critical value of the test statistic?
3. Use Excel’s pivot table feature to summarize the data into a contingency (cross-tabulation) table.
4. Calculate the expected cell frequencies.
5. Compute the calculated value of the test statistic.
6. State your conclusion. What is your conclusion as to whether there is or is not a relationship between the two variables?

Answer 1

Answer:

A random sample of 303 individuals collected the following information: sex, marital status, age, country, size, and type. The variables marital status and type (which refers to type of automobile—either family, sporty, or work) are of interest to us. We would like to know if there is a relationship between the two qualitative variables marital status and type. We will test our hypothesis at the α = 0.01 level of significance

1. State the hypotheses of interest.

Ho: there is no relationship between marital status and type

H1: there is a relationship between marital status and type

2. How many degrees of freedom will the test have? What is the critical value of the test statistic?

Df= (2-1)(3-1)=2

Critical value =9.21

3. Use Excel’s pivot table feature to summarize the data into a contingency (cross-tabulation) table.

Count of Marital Status	Type
Marital Status	Family	Sporty	Work	Grand Total
Married	119	45	32	196
Single	36	55	16	107
Grand Total	155	100	48	303

4. Calculate the expected cell frequencies.

Expected Frequencies
	Column variable
Row variable	Family	Sporty	Work	Total
Married	100.2640	64.6865	31.0495	196
Single	54.7360	35.3135	16.9505	107
Total	155	100	48	303

5. Compute the calculated value of the test statistic.

Calculations
fo-fe
18.7360	-19.6865	0.9505
-18.7360	19.6865	-0.9505
(fo-fe)^2/fe
3.5011	5.9913	0.0291
6.4133	10.9747	0.0533

Calculated chi square = 26.9629

6. State your conclusion. What is your conclusion as to whether there is or is not a relationship between the two variables?

Calculated chi square = 26.9629 > critical chi square 9.21, Ho is rejected. we conclude that there is a relationship between marital status and type.