A student team examined parked cars in four different suburban shopping malls. One hundred vehicles were examined in each location. Research question: At á = .05, does vehicle type vary by mall location?

Vehicle Type Somerset Oakland Great Lakes Jamestown Row Total
Car 44 49 36 64 193
Minivan 21 15 18 13 67
Full-sized Van 2 3 3 2 10
SUV 19 27 26 12 84
Truck 14 6 17 9 46
Col Total 100 100 100 100 400

To determine whether vehicle type varies by mall location, you can use a chi-square test of independence. This test compares the observed frequencies of each combination of mall location and vehicle type with the frequencies you would expect if there was no relationship between the two variables.

To perform the chi-square test, follow these steps:

1. Set up the null and alternative hypotheses:
- Null hypothesis (H₀): Vehicle type and mall location are independent.
- Alternative hypothesis (H₁): Vehicle type and mall location are dependent.

2. Calculate the expected frequencies for each combination of vehicle type and mall location under the assumption of independence. To do this, multiply the row total for each vehicle type by the column total for each mall location and divide by the overall total.

For example, the expected frequency for "Car" in "Somerset Mall" would be (193/400) * (100/400) * 400 = 48.25.

3. Calculate the chi-square statistic. This is the sum of the squared differences between the observed and expected frequencies, divided by the expected frequencies.

For each combination of vehicle type and mall location, calculate (Observed - Expected)² / Expected. Sum these values across all combinations to obtain the chi-square statistic.

4. Determine the degrees of freedom. This is calculated as (number of rows - 1) * (number of columns - 1). In this case, the degrees of freedom would be (5 - 1) * (4 - 1) = 12.

5. Look up the critical chi-square value in a chi-square distribution table for the given significance level (α). The degrees of freedom will determine the appropriate table to use. In this case, with α = 0.05 and 12 degrees of freedom, the critical chi-square value is approximately 21.03.

6. Compare the calculated chi-square statistic to the critical chi-square value. If the calculated chi-square statistic is greater than the critical value, reject the null hypothesis and conclude that there is a relationship between vehicle type and mall location.

7. Calculate the p-value associated with the calculated chi-square statistic. This can be done using a chi-square distribution calculator or a statistical software. If the p-value is less than the chosen significance level (α), reject the null hypothesis.

Please note that the calculated chi-square statistic and p-value for this specific example are not provided. You would need to perform the calculations using the given data.