Twitter: Suppose that the population proportion of Internet users whosay they use Twitter or a similar service to post updates about themselves or to see updates about others is 19%. Think about selecting random samples from a population in which 19% are Twitter users.
a) Describe the sample space for selectin a single person.
b) If you select 3 people, describe the sample space.
c) Using the results from ‘b’ define the sample space for the random variable that expresses the number of Twitter users in the sample of size 3.
d) What information is contained in the sample space for part b that is not contained in the sample space for part c. Do you think this information is important? Explain.
a) The sample space for selecting a single person from the population is {Twitter user, Non-Twitter user}, as there are only two possible outcomes: individuals who use Twitter or a similar service, and those who do not.
b) The sample space for selecting 3 people would be all possible combinations of Twitter users and non-Twitter users. It can be represented as {(Twitter user, Twitter user, Twitter user), (Twitter user, Twitter user, Non-Twitter user), (Twitter user, Non-Twitter user, Twitter user), (Twitter user, Non-Twitter user, Non-Twitter user), (Non-Twitter user, Twitter user, Twitter user), (Non-Twitter user, Twitter user, Non-Twitter user), (Non-Twitter user, Non-Twitter user, Twitter user), (Non-Twitter user, Non-Twitter user, Non-Twitter user)}.
c) The sample space for the random variable that expresses the number of Twitter users in the sample of size 3 will consist of all possible values of the number of Twitter users in a sample of 3. It can be represented as {0, 1, 2, 3}.
d) The sample space for part b provides information about the specific combinations of Twitter users and non-Twitter users in a sample of size 3. On the other hand, the sample space for part c only provides information about the possible number of Twitter users in the sample, without specifying the specific combinations. The information in part b's sample space is important as it allows for a more detailed understanding of the distribution of Twitter users in the sample, whereas part c's sample space simplifies the analysis to focus solely on the number of Twitter users.