Question

It is believed that 35% of the US population owns one car, 30% own two cars, 25% own three cars or more, and 10% do not own a car. You want to take a simple random sample of individuals to test this claim. What is the smallest number of people required for the sample to meet the conditions for performing inference

Answer 1

Answer: 50 is the answer.

Explanation:

35% of U.S population owns a car=

35/100= 0.35

30% owns two cars= 30/100= 0.30

25% owns 3 or more cars= 25/100= 0.25.

The smallest number of people required for the sample to meet the conditions for performing inference is given below:

Here, the minimum percentage is for those who do not own a car = 10 / 100= 0.10

Therefore for each cell, there must be atleast expected 5 counts.

so if n is requisite sample size than

Expected number of people who do not own a car = 0.10 n

that value must be greater than 5

so,

0.10n > or = 5

n>= 5/0.10

n > = 50

so here 50 is the answer.