Question

Example 2:
An example that you might encounter in your everyday life is Nielsen TV Ratings. Analyses of the mass media are common in the social sciences, as they are a prime agent of socialization and an enormous industry worldwide. The Nielsen Household Rating is not based upon the quality of a given program but solely on viewership. It depicts the percentage of a potential audience who are watching a particular television program (as opposed to watching other programs or doing other activities such as housework). Using set metering equipment that attaches a “black box” of sorts to their TV set, cable box, and satellite dish, information is sent nightly to Nielsen's central computers. While techniques to measure media use have been rapidly changing to what they call “Total Audience Measurement over the past few years due to the nature of media use (DVR, smartphones, etc.), in order to measure live TV viewing Nielsen has traditionally relied on set meters to sample about 5,000 Households (containing 13,000 people) at any one given time. People are often quite surprised that such a small sample of just a few thousand people can determine whether Dancing with the Stars, Survivor, or any of your other favorite shows is kept on the air or gets cancelled. How is it possible that such a small number of people can essentially “speak for" or represent over 300 million Americans, or 33 million Canadians, and so forth?
Referring to Example 2 in the section above, suppose that a smaller sample size was used to conduct Nielsen ratings. What would the margin of error be (assume it is a ± value, in %) for a 95% confidence interval with a sample size of just 200 cases?

Answer 1

Given that n200 No Prior Inturmatiun is given about estimate we will take P 0.50 Margin ofemr Z PCI-P) Zoi025 O.50X0.50 200 Zay usin1 Ztable (1-96) (0.0354) 0.0694 is O.0694 Margin of enmr This is 6.94 %