Question

An analyst at a local bank wonders if the age distribution of customers coming for service at his branch in town is the same as at the branch located near the mall. He selects 100 transactions at random from each branch and researches the age information for the associated customer. Use the table below to answer the questions.

	Less than 30	30-55	56 or older	Total
In-town branch	20	42	38	100
Mall branch	30	48	22	100
Total	50	90	60	200

1. What are the null and alternative hypotheses?

a. Ho: The age distributions of customers at the two branches are not the same.

     Ha: The age distributions of customers at the two branches are the same.

b. Ho: Age is not independent of branch.

    Ha: Age is independent of branch.

c. Ho: The age distributions of customers at the two branches are the same.

    Ha: The age distributions of customers at the two branches are not the same.

d. Ho: Age is independent of branch.

    Ha: Age is not independent of branch.

2. What type of test is this?

a. Chi-square goodness-of-fit-test

b. Chi-square test of independence

c. Chi-square test of homogeneity

3. What are the expected numbers for each cell if the null hypothesis is true?

	Less than 30	30-55	56 or older	Total
In-town branch				100
Mall branch				100
Total	50	90	60	200

4. Find the X2 statistic.

X2 =               (round to two decimal places)

5. How many degrees of freedom does the X2 statistic have?

df =

6. Find the critical value at alpha = 0.05

X2 =               (round to three decimal places)

7. What do you conclude?

The test statistic is (greater than or less than) the critical value. There is (insufficient or sufficient) evidence to reject Ho.

Answer 1