Suppose you are a television network executive interested in how a new pilot show, Stat1stics, will be received by the general US 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 Stat1stics. Each firm then gathers nine respondents and asks each of them, "On a scale of 1 to 10, where 1 means you’ll never watch Stat1stics again, and 10 means you expect to never miss an episode of Stat1stics, how do you rate Stat1stics?"

Assume that if you asked every member of the general US television-viewing population about the pilot, the mean response would be 4.0 with a standard deviation of 1.2.

Each market research firm reports the mean rating of its random sample. Assume each market research firm recruits a different sample, and that you hired exactly enough market research firms such that all possible samples of nine US 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 firms? Check all that apply.
i. The standard deviation of the distribution of mean ratings is 0.13.
ii. The central limit theorem does not provide justification to assume that the shape of this particular distribution of mean ratings is normal.
iii. The standard error of the mean ratings is 1.2.
iv. The mean of the distribution of mean ratings is 4.0.