Question

A marketing director of a soft drink company wants to know what proportion of its potential U.S. customers have heard of a new brand. The company has access to a database with the mobile phone numbers of 10,000 U.S. college students. The director’s assistant asks a simple random sample of 50 students from this database whether they heard of the new soft drink brand, and constructs the sample proportion. 1 (a) What is the target population? (b) What is the sampled population? (c) Will the sample proportion be unbiased for the proportion in the sampled population? Explain. (d) Will the sample proportion be unbiased for the proportion in the target population? Explain.

Answer 1

1 (a) Target Population:

Ans : U.S. Population

As the marketing director of a soft drink company wants to know what proportion of its potential U.S. customers have heard of a new brand

(b) What is the sampled population?

Ans : 10,000 U.S. college students

As the sample is taken  from 10,000 U.S. college students

(c)

(c) Will the sample proportion be unbiased for the proportion in the sampled population? Explain

Yes. As the this sample is a simple random sample taken from the population of from 10,000 U.S. college students: the sampled population ;

So this sample represents the the sampled population ;

So, the sample proportion is a unbiased for the proportion in the sampled population.

(d) Will the sample proportion be unbiased for the proportion in the target population

No. this sample is a simple random sample taken from the population of from 10,000 U.S. college students. And this sample does not represent target population which is the entire US population.

Hence the sample proportion will be a biased for the proportion in the target population