Have you ever been disappointed because a television network cancelled one of your favourite television shows because of "low ratings"? The network didn't ask your opinion, did it? It probably didn't ask any of your friends, either. That's because estimates of television audience sizes are based on research done by the Nielsen Company, which uses a sample of 9,000 households out of the more than 113 million households in the United States to determine national ratings for television programs. That doesn't seem like enough, does it? As it turns out, statistically, it's significantly more than enough.
1. Go to https://www.surveysystem.com/sscalc.htm to determine the appropriate sample size for a population of 113 million households. Assuming a confidence interval of 5, how large should the sample of households be if desiring a 95 percent confidence level? How large for a 99 percent confidence level? Briefly explain what is meant by confidence interval and confidence level.
2. What sample sizes are necessary at population sizes of 1 billion, 10,000, and 100 with a confidence interval of 5 and a 95 percent confidence level? Explain the effect population size has on sample size.