Question

It is believed that 36% of the US population has never been married, 32% are divorced, 27% are married, and 5% are widowed. 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: the smallest number of people required for the sample to meet the conditions for performing inference is 100

Explanation:

Given that;

36% of US population has never been married

32% are divorced

27% are married

5% are widowed

Taking a simple random sample of individuals to test this claim;

we need expected count in each cell to be at least 5, here the smallest proportion is 5% = 0.05

so we only need to satisfy condition for its expected count;

n × 0.05 ≥ 5

n = 5 / 0.05 = 100

Therefore the smallest number of people required for the sample to meet the conditions for performing inference is 100