Question

# 4. Before the Christmas rush began, a department store noted that the percentages were the same...

4. Before the Christmas rush began, a department store noted that the percentages were the same for their customers who used the store’s credit card, a major credit card, and those people who paid cash (each was .333). In a sample of 150 people shopping during the Christmas rush, 46 used the store’s credit card, 43 used a major credit card, and 61 paid cash.
Test to see if the methods of payment have changed during the Christmas rush. Use a .05 level of significance.

Solution: The null and the alternative hypotheses are given below:

The methods of payment have not changed during the Christmas rush.

The methods of payment have changed during the Christmas rush.

Under null hyptothesis the test statistic is:

Where:

is the observed frequency

is the expected frequency

We are given:

Now at 0.05 significance level and for is given below:

Since , we therefore fail to reject the null hypothesis and conclude that the methods of payment have not changed during the Christmas rush.

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