# Approximate 95% confidence interval- Practice exam question

#### rebecca1993

##### New Member
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
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:
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).

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#### Dason

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).

#### rebecca1993

##### New Member
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 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?

#### GretaGarbo

##### Human
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.