Approximate 95% confidence interval- Practice exam question

#1
Hi there,
I have end of semester exams coming up and my tutor has posted an example exam. One of the example questions is as follows:

A study of 113 dead pelicans found that 47 had foreign objects in their gut. An approximate 95% confidence interval for the population proportion of pelicans with foreign objects in their gut is:
(A) 0.416 +- 0.0464
(B) 0.416 +- 0.139
(C) 0.416 +- 0.0909
(D) 0.416 +- 0.0927
(E) 0.416 +- 0.119

Now we know the answer is (D) however nobody in my study group knows how to get it. Even my private tutor couldn't help on this one. Any help and assistance would be appreciated.
 

ondansetron

TS Contributor
#2
Hi there,
I have end of semester exams coming up and my tutor has posted an example exam. One of the example questions is as follows:

A study of 113 dead pelicans found that 47 had foreign objects in their gut. An approximate 95% confidence interval for the population proportion of pelicans with foreign objects in their gut is:
(A) 0.416 +- 0.0464
(B) 0.416 +- 0.139
(C) 0.416 +- 0.0909
(D) 0.416 +- 0.0927
(E) 0.416 +- 0.119

Now we know the answer is (D) however nobody in my study group knows how to get it. Even my private tutor couldn't help on this one. Any help and assistance would be appreciated.
I think more or less C and D can be too dependent on rounding, so how do you know D is correct?

I would suggest 3 things:
1) Get your money back from your private tutor.
2) Fire your private tutor
3) Post on here the formula you think might be useful for developing a confidence interval for a binomial proportion

We're happy to help if you show some work (and I haven't commented on what is right or wrong, here).
 
Last edited:

Dason

Ambassador to the humans
#3
I think C would be the typical answer if not for the word "approximate". That alone makes me think they want them to use 2 instead of the slightly more exact 1.96 when constructing the interval and in using 2 that does lead to (D).
 
#4
Yes that’s correct, they want us to use 2 rather than 1.96. And I am saying D is correct based on what the university tutor has marked as the correct answer on the practice exam.
I think I’ll be taking your advice on firing my tutor.
I am using formula p+-z* square root of p(1-p)/n
Because I only have a sample proportion and a sample size is that correct?
Is this the same formula you used to get (D) Dason?
 
#5
I think C would be the typical answer if not for the word "approximate". That alone makes me think they want them to use 2 instead of the slightly more exact 1.96 when constructing the interval and in using 2 that does lead to (D).
Yes, I thought that the “approximation” word was because the binomial distribution is approximated by the normal distribution.

It could have been fun to be in that class and be a contrarian. Whatever the teacher or tutor says you suggest something else, like Agresti-Coull or Clopper-Pearson.

But if this is supposed to teach people something about statistics in reality, you should ask why on the earth should the number of dead pelicans be an independent random sample with binomial distribution from the total population of pelicans? Maybe they have died just because they have foreign objects in their gut. Maybe the living population has 10% with objects in their gut?

My answer would be, we don’t know.

Statistics is supposed to help you, not misguide you.
 

ondansetron

TS Contributor
#6
Yes, I thought that the “approximation” word was because the binomial distribution is approximated by the normal distribution.

It could have been fun to be in that class and be a contrarian. Whatever the teacher or tutor says you suggest something else, like Agresti-Coull or Clopper-Pearson.
I considered this at first as maybe why "they couldn't arrive at the answer" in the event the class covered some other method of calculating the interval like AC or CP but the tutor "went by the standard z approximation." Like @Dason, I got C without rounding anything and then D with rounding 1.96 to 2.

@rebecca1993 You are correct with that formula. I wanted you to find it and work with the numbers to see what answer you come up with! The difference between C and D is using 1.96 for z versus the number 2 (which some people do for convenience/mental math). Although I'm sure @Dason uses 1.96 and unrounded numbers for mental math and carries the calculation to 9 decimal places with accuracy in his head o_O.