Quiz #5
The answer is given in the answer box below.
Scroll down for an explantion for the answer (given in red).
Be sure to put your name on this quiz. Write the letter corresponding
to the correct answer in the answer box below.
Suppose that 30 iid Bernoulli trials are observed, and the observations
consist of 10 successes and 20 failures.
A decent approximate 99% confidence interval for
the probability of success, p, is (0.16, 0.57). Based on this interval
estimate of p, which of the following statements is clearly true?
(Note: Two of the statements are clearly false. Two other
statements could be true --- that is, it's impossible to state
whether they are true or false based on the information given.
But one statement is without a doubt true.)
- [ A ] 0.33 is the value of p
- [ B ] 0.16 < p < 0.57
- [ C ] P( 0.16 < p < 0.57 ) = 0.99
- [ D ] the interval obtained is possible if p = 0.6
- [ E ] a decent 90% confidence interval for p will be wider
-
[ D ] is true --- it is certainly possible to obtain 10 outcomes of success and 20 outcomes of failure if
p is equal to 0.6.
- [ A ] and [ B ] could be true, but since it is possible to
obtain 10 outcomes of success and 20 outcomes of failure if
p is any value between 0 and 1, we cannot rule out other values for
p that don't satisfy [ A ] or [ B ].
- [ C ] and [ E ] are clearly false.
- There are no random variables involved with the
event 0.16 < p < 0.57, and so
P( 0.16 < p < 0.57 ) is either 0 or 1. (0.16, 0.57, and p are all constants ---
the value of p is unknown, but it isn't random.)
- A 95% confidence interval will be wider than a 90% confidence interval ---
not the other way around! (To increase the probability of coverage, the interval has to be made wider --- if a decreased coverage
probability is acceptable, a narrower interval can be used.)