Question

Q1. [7 Marks] In some states in the U.S., the law requires drivers to have their headlights in daytime when driving under the rain. A highway patrol officer would like to investigate what percentage of drivers is following the rule. A random sample of 200 cars on a rainy afternoon was drawn and 74 of them have their headlights on.

a) Identify the subjects of interest. [1]

b) Suggest a name for the variable of interest. [1]

c) Identify the type of variable. [1]

d) Identify the scale of measurement. [1]

e) Provide a description of an appropriate statistic. [2]

f) Report the value of the statistic you described in part

Answer 1

Solution :

a) The subjects of interest are the drivers in some states of U.S who drives in rainy afternoon.

b) The variable name is "Headlights in rainy afternoon".

c) This is a categorical variable. It has two possible categories. One category contains the drivers whose vehicle's headlight is on in rainy afternoon and other category contains the drivers whose vehicle's headlight is not on in rainy afternoon.

d) The scale of measurement is nominal.

e) The appropriate statisic would be sample proportion. By this statisic we can have idea about the proportion of drivers whose headlights are on in rainy afternoon. The sample proportion is given by,

Where, X is the number of drivers whose vehicle's headlight is on in rainy afternoon and n is total number of drivers in the sample.

f) We have, X = 74 and n = 200

The value of the statisic is 0.37.