A restaurant has a jar of red and white gumballs by the cash register, and invites customers to guess the proportion of red gumballs. Of the 55 gumballs that you can see, you count 34 red ones. Give a 90% confidence interval for the proportion of red gumballs in the jar, using the large-sample method.

[ Select ] [.549 to .797, .569 to .777, .490 to .747, .510 to .726, "something else"]

Suppose you had counted 49 red gumballs out of 55. Why would a plus-four confidence interval be preferable to a large-sample confidence interval in that case?

[ Select ] ["There are fewer than 15 successes.", "There are fewer than 15 failures.", "The confidence level is too low.", "The sample size is smaller than 10, so we can't even use the plus-four method.", "We should use t-statistics in that case."]