Question

Buyers of three different brands of automobiles were asked if they would buy the same brand again. 100 individuals were surveyed for each brand to determine if there is a significant difference among the brands regarding future purchase possibilities. The results were:

Purchase Again?      City A        City B        City C        Total

Yes                          20              25              30              75

No                           80                75              70             225

Total                       100              100            100            300

Is there evidence of a significant difference among the groups with respect to willingness to purchase the brand of car again? (use alpha=.05)

Answer 1

Here we have to test the hypothesis that,

H0 : Brands of automobiles and buying the brand again are independent.

H1 : Brands of automobiles and buying the brand again are dependent.

Assume alpha = level of significance = 0.05

The test statistic follows X²-distribution with (R-1) (C-1) degrees of freedoms.

where R is number of rows

C is number of columns

We can do this test in MINITAB.

steps :

ENTER data into MINITAB sheet --> Stat --> Tables --> Chi square test for association --> summarized data in a two way table --> Columns containing the table : select all the data together --> Ok

————— 21-06-2019 19:23:09 ————————————————————

Welcome to Minitab, press F1 for help.
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Chi-Square Test for Association: Worksheet rows, Worksheet columns

Rows: Worksheet rows Columns: Worksheet columns

C1 C2 C3 All

1 20 25 30 75
25 25 25

2 80 75 70 225
75 75 75

All 100 100 100 300

Cell Contents: Count
Expected count

Pearson Chi-Square = 2.667, DF = 2, P-Value = 0.264
Likelihood Ratio Chi-Square = 2.681, DF = 2, P-Value = 0.262

Test statistic = 2.667

P-value = 0.264

df = 2

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : Brands of automobiles and buying the brand again are independent.