Question

You work in a very large metropolitan police department and have been assigned to a committee to select new patrol cars. Three models are in contention.

The Dodge Charger

The Chevrolet Tahoe

The Ford Interceptor

Your initial testing determines that all three models meet your department’s basic needs and that they are all comparably priced. So, the final decision really is based on the personal preference of the officers.

You and the members of your committee send out a simple survey asking each officer to indicate which of the three models he or she prefers. This survey indicates the following.

Vehicles	Percent of officer preference
The Dodge Charger	45%
The Chevrolet Tahoe	42%
The Ford Interceptor	13%
Totals	100%

Given the closeness of officer preference between the Dodge Charger and Chevrolet Tahoe it will be important now to determine whether the differences in preference are statistically significant, i.e. not due to chance. You start with a hypothesis.

The difference in officer preference between the Dodge Charger and Chevrolet Tahoe is statistically significant.

Answer the following questions.

1. What type of hypothesis is this (association or difference)? (Hint: the answer lies in the hypothesis)

2. Officer preference is the variable and its attributes are Charger, Tahoe and Interceptor. At what level (nominal, ordinal or scale) is this variable measured?

3. Using the handout titled “The Statistical Decision” (located in the Resources tab of the TRACS site, see section 1c) which statistical technique would be the most appropriate technique for analyzing these data?

Answer 1

This is a simple problem related to the hypothesis testing of difference between two mean proportions.

Here we are given with proportions of 45 % and 42% . Hence we take sample sizes of each to be equal to 100.

We have hence analysed the data and found that the difference of the proportions is not significant .

We used the hypothesis testing of difference of the mean proportion of samples .

Clearly the respondants are required to select between three defined options of

The Dodge Charger

The Chevrolet Tahoe

The Ford Interceptor

Hence the variables are clearly nominal .This is so because

All the given variables are mutually exclusive (no overlap) and none of them have any numerical significance.

We used the statistical technique of hypothesis testing to analyse the data set.