Suppose that the researchers at Vermont Outlet, Inc. (“VO”) additionally want to

Question

Suppose that the researchers at Vermont Outlet, Inc. (“VO”) additionally want to investigate the relationship between a respondent’s having previously ordered merchandise from the VO catalog and a respondent’s household income. But instead of using V4 as the measure of having previously ordered merchandise, the researchers use the variable V46 instead, where:

V46: “Have you ever ordered any merchandise from the VO catalog?”

         1 = no

2 = yes

The measure of household income (V45) is as follows:

V45: “Household income” is defined as:

         1 = under $75,000

2 = over $75,000

Below are questions pertaining to testing the hypothesis of independence between V46 and V45, and interpreting the contingency table.

(i) _______ What percentage of high income households have ever ordered merchandise from the VO catalog?  

(ii) _________ What percentage of low income households have ever ordered merchandise from the VO catalog?

(iii) Is the association between V45 and V46 statistically significant (at the 0.05 level of significance)? Answer “yes” or “no” and then explain exactly the basis of your answer.

________________________________________________________

(iv) In light of your answer to part (iii) above, interpret the difference in values between your answers to part i and part ii above (be specific).

_____________________________________________________________

_____________________________________________________________

Crosstabs Case Processing Summary Cases Missing Tota Percent Percent Percent V45* V46 122 98.4% 1.6% 124 100.0% V45 * V46 Crosstabulation V46 1.00 2.00 Tota 63 100.0% 51.6% 51.6% 59 100.0% 48.4% 48.4% 122 100.0% 100.0% 100.0% V45 1.00 Count 39 61.9% 48.8% 32.0% 41 69.5% 51.3% 33.6% 80 65.6% 100.0% 65.6% % within V45 % within V46 % of Total 24 38.1 % 57.1 % 19.7% 2.00 Count % within V45 % within V46 % of Total Count % within V45 96 within V46 % of Total 30.5% 42.9% 14.8% 42 34.4% 100.0% 34.4% Tota Chi-Square Tests Asymptotic Significance Exact Sig. (2 Exact Sig. (1 sided) Value df (2-sided) sided) Pearson Chi-Square Continuity Correction" Likelihood Ratio Fisher's Exact Test Linear-by-Linear 777a 477 779 378 490 377 447 245 770 380 Association N of Valid Cases 122 a. 0 cells (0.0%) have expected countless than 5, The minimum expected count is 20.31 b. Computed only for a 2x2 table

Explanation / Answer

Answer:

Below are questions pertaining to testing the hypothesis of independence between V46 and V45, and interpreting the contingency table.

(i) _______ What percentage of high income households have ever ordered merchandise from the VO catalog?  

69.49%

(ii) _________ What percentage of low income households have ever ordered merchandise from the VO catalog?

61.90%

(iii) Is the association between V45 and V46 statistically significant (at the 0.05 level of significance)? Answer “yes” or “no” and then explain exactly the basis of your answer.

No.

The calculated chi square = 0.777, P=0.378 which is > 0.05 level of significance. Null hypothesis is not rejected.

(iv) In light of your answer to part (iii) above, interpret the difference in values between your answers to part i and part ii above (be specific).

The percentage of high income households have ever ordered merchandise from the VO catalog is 69.49% and low income group is 61.9%. Even though there is a difference in percentages, it is not statistically significant.

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