Question

Before the rush began for Christmas shopping, a department store had noted that the percentage of its
customers who use the store's credit card, the percentage of those who use a major credit card, and the
percentage of those who pay cash are the same. During the Christmas rush in a sample of 150 shoppers,46 used the store's credit card; 43 used a major credit card; and 61 paid cash.

With ? = 0.05, conduct a
complete and appropriate hypothesis test to see if the methods of payment have changed during the
Christmas rush.

Use the 5-step procedure discussed in class and the critical value approach. If and
only if it is appropriate to do so, offer an informal comment as to where the single largest change is.

Answer 1

5-step procedure for hypothesis testing using the critical value approach:

Step 1 : To state the null hypothesis (H₀) and alternate hypothesis (H₁),

H₀:During christmas rush, all three modes of payment (using store credit card, major credit card and cash payment) are equally common.

Vs

H_1:During christmas rush, three modes of payment (using store credit card, major credit card and cash payment) change significantly.

Step 2: Test statistic and level of significance

Test statistic Chi square for comparision of multiple proportions

where p_i = Proportion observed

p_exp = Proportion expected (In accordance with null hypothesis)

n_i = Frequency

The level of significance commonly chosen for consumer research project is 0.05.

Step 3 : Decision rule

Compare the test statistic value obtained, with its critical value obtained from chi square tables for 0.05 probability and 2 degrees of freedom(df) .Here df i= no.of samples compared - 1

If the observed value exeeds the tabled one, it is concluded that there is little evidence to support the claim that all three modes of payment (using store credit card, major credit card and cash payment) are equally common.

Step 4: Computation of test statistic and decision making

Using R,

Using SPSS,

Analyse-> Non-parametric tests->Legacy dialog->Chi square

So = 3.720 with p value 0.156.So, there is enough evidence to support the claim that all three modes of payment (using store credit card, major credit card and cash payment) are equally common.

Step 5: Conclusion

We may conclude that even during christmas rush, all three modes of payment (using store credit card, major credit card and cash payment) are equally common.