The following table represent the number of dogs per household in a small town. Dogs 0 1 2 3 4 5 Households 1491 425 168 48 29 14

Question

Given x={0,1,...,5} Are any the these events unusual? Explain.

Answer 1

Dogs 0 1 2 3 4 5

Houses 1491 425 168 48 29 14 Total 2175

Frequency 0.686 0.195 0.077 0.022 0.013 0.006

Compute the frequency distribution of x, e.g. for 0 dogs, frequency = 1491/2175).

An "unusual" event would be one that does does typically happen. If we use a frequency of 0.05 as the cut-off point for making an event "unusual", then having 3 or more dogs would be an "unusual" event. If we use a more strict frequency of 0.01 as the cut-off point, then having 5 dogs would be an "unusual" event.

Answer 2

First let's determine how many households are included in this obeservational study.

Simply add up the number of households with 0, 1, 2, 3, 4, and 5 dogs. [2175]

Next, calculate the proportion of households with "x" number of dogs. For example, the proportion of households with 1 dog is (the number of households with one dog) / (the total number of households). 425/2175 = 0.195 or 19.5%

Calculate the proportions for all possible values of x. (BTW if this is a probability distribution, the total proportions must add up to 1.)

In statistics we usually define an 'unlikely event' as event with a probability of less than 0.05 or 5%. We can see from our analysis that households with more than 2 dogs are unusual.