2. Applying the central limit theorem

2. Applying the central limit theorem Suppose you are a television network executive interested in how a new pilot show, Statistics, will be received by the general U.S. television-viewing population. You hire several market research firms; each recruits a random sample of television viewers and asks them to watch the pilot of Statistics. Each firm then gathers 9 respondents and asks each of them, \"On a scale of 1 to 10, where 1 means you'll never watch Statistics again, and 10 means you expect to never miss an episode of Statistics, how do you rate Statistics?\" Assume that if you asked every member of the general U.S. television-viewing population about the pilot, the mean response would be 6.5 with a standard deviation of 1.5. Each market research rm reports the mean rating of its random sample. Assume each market research rm recruits a different sample, and that you hired exactly enough market research rms such that all possible samples of 9 U.5. television viewers were sampled and their mean ratings reported. Which of the following are true about the sampling distribution of the mean ratings reported to you by the market research rms? Check all that apply. The central limit theorem suggests that the shape of this distribution of mean ratings is approximately normal. The shape of the distribution of mean ratings depends on how many respondents each market research company recruits. C C I: The mean of the distribution of mean ratings is 2.17. C The standard error of the mean ratings is 0.50. If you were really a television network executive, you would not hire multiple market research rms to each recruit a different sample of respondents. Instead, you would likely hire only one market research firm. If this is the case, why should you care about the theoretical distribution of mean ratings of multiple samples if you are only going to hire one firm and get one sample and one mean from that sample? Q You should not care about the possible distribution of mean ratings. You should only care about the mean and perhaps the highest and lowest ratings. 0 You need to know the theoretical distribution of possible values of the sample mean ratings to know whether the market research rm recruited the right sample. O To draw conclusions about the population mean using a sample mean, you need to know the theoretical distribution of the possible values the sample mean ratings could have