A survey of 1052 adults found that 53% classified themselves as "very happy" when given the choices of "very happy," "fairly happy," or "not too happy." Suppose that a journalist took advantage of this poll to write the headline: "More than 50% of U.S. adults classify themselves as 'very happy'." a. If p = true population proportion of all U.S. adults who were very happy in 2000, test whether the headline is justified. Use a significance level of 0.01. Make sure to check any necessary conditions. b. If in fact the true proportion of U.S. adults classify themselves as very happy is NOT 50%, what type of error would the journalist have committed?