An analyst at a local bank wonders if the age distribution ofcustomers coming for service at his branch in town is the same asat the branch located near the mall. He selects 100 transactions atrandom from each branch and researches the age information for theassociated customer. Use the table below to answer thequestions.
| 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 branchesare not the same.
Ha: The age distributions of customersat 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 branchesare the same.
Ha: The age distributions of customers at thetwo 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 nullhypothesis 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 criticalvalue. There is (insufficient or sufficient) evidence to rejectHo.
