An analyst wonders if the age distribution of customers coming for service In Town is the same as at the Mall.

He selects transactions at random from each branch and researches the ages of the customers. These are the data :

Age

< 30

30 - 55

56 +

Totals

Distribution

In Town

24

37

35

96

Mall

29

49

30

108

Totals

53

86

65

204

For all problems, try to enter your answers or calculations in the yellow cells.

1

Write the null hypothesis regarding the frequency distribution of ages by In Town and Mall.

Null Hypothesis (H): There is no significant difference in the distribution of ages among bank locations (town and mall branches). The null hypothesis assumes that the observed distribution is consistent with the expected distribution. The alternate hypothesis is that there is a difference or that the age distribution at the town branch differs from that of the mall branch.

Which type of test is required (goodness of fit, independence, homogeneity)?

Goodness of fit because this test is a way of determining whether a set of categorial data (age distribution of customers coming from in town or mall location) came from a claimed discrete distribution or not.

2

Compute

Age Groups

< 30

30 - 55

56 +

Expected (E)

In Town

Mall

Age Groups

< 30

30 - 55

56 +

(O - E)2/E

In Town

Mall

3

What is the chi square test statistic? Note: =CHISQ.TEST does not compute the chi-squared test statistic. It computes p-value.

4

What is the degrees of freedom of the chi-squared test statistic?

Use an Excel function to compute the critical value at alpha = 10%.

What is the percent p-value of the chi square test statistic?

5

State your decision about H0 with the significance level.

Are the bank distributions the same (Yes/No)?