Question

1. A marketing firm wants some data on how marital status and store preference are related. To get a first approximation of this problem, data are gathered as to preference of box stores vs small storefronts in malls and towns. The following data are obtained from 200 individuals.

	Single	Married	Divorced	Widowed
Prefer Box stores	40	10	35	15
Prefer other types of stores	15	30	25	30

1. What type of data is represented in the table? Explain.
2. What is the null hypothesis?
3. Calculate the expected values for each cell, assuming the null hypothesis is true.
4. Complete the 5-step procedure for hypothesis testing using α = .05.
5. What conclusions can be made?

Answer 1

a.

The data contained in the table is categorical. This is because we have the data divided by the marital status into four categories: Single, married, divorced and widowed.

b.

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0​: The two variables - marital status and store preference are independent

Ha​: The two variables - marital status and store preference are dependent

This corresponds to a Chi-Square test of independence.

c.

The following cross-tabulation has been provided. The row and column total have been calculated and they are shown below:

	Column 1	Column 2	Column 3	Column 4	Total
	40	10	35	15	100
	15	30	25	30	100
Total	55	40	60	45	200

d.

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0​: The two variables are independent

Ha​: The two variables are dependent

This corresponds to a Chi-Square test of independence.

Rejection Region

Based on the information provided, the significance level is α=0.05 , the number of degrees of freedom is df=(2−1)×(4−1)=3, so then the rejection region for this test is R={χ2:χ2>7.815}.

Test Statistics

The Chi-Squared statistic is computed as follows:

Decision about the null hypothesis

Since it is observed that χ2=28.03>χc2​=7.815, it is then concluded that the null hypothesis is rejected.

P-Value

The corresponding p-value for the test is

e.

Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables - marital status and store preference are dependent, at the 0.05 significance level.

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