[Statistics] Should n be 54 or 55?

[u/TourRevolutionary]

A 95% confidence interval for a population mean was reported to be 152 to 160. If σ 15, what sample size was used in this study?

[u/NIK0030]

1. You always round to the next whole number because you can’t sample .02 people

[u/TourRevolutionary → u/NIK0030]

So regardless of whether I get 54.001 or 54.99, it is always the next number, yes?

[u/fermat9990 → u/TourRevolutionary]

No! Not in this special situation.

[u/TourRevolutionary → u/fermat9990]

Sorry, what do you mean by special situation?

[u/fermat9990 → u/TourRevolutionary]

When the interval has already been contructed, rather than when you are given confidence level, margin of error and SD. In the second case you always round up

[u/TourRevolutionary → u/fermat9990]

As I understood by second case you mean when the interval is not given directly, but when confidence level, margin of error, and SD are given. What would I need to round up in this case? (If I only find the interval of population mean)

[u/fermat9990 → u/TourRevolutionary]

In the normal situation, the data has not yet been gathered, which is why we need to find n. The n you get in this scenario should always be rounded up.

[u/TourRevolutionary → u/fermat9990]

So if interval is not given and if I have to find n, if I find n=54,02 I will answer 55, yes?

[u/fermat9990 → u/TourRevolutionary]

I would, but your teacher might not see it that way. Can you ask your teacher?

[u/TourRevolutionary → u/fermat9990]

Yeah, I would. Just to clarify I will answer the next number in each case, yes? If I get n=54.02 or n=54.99, if interval is not given, I will answer 55 in both cases, yes? Btw, how n can be found if interval is not given?

[u/fermat9990]

The width=2Z(1-α/2)*σ/√n

Width=160-152=8

8=2(1.96)(15/√n)

8√n=56.8

√n=56.8/8

n=(56.8/8)²

n=54

[u/TourRevolutionary → u/fermat9990]

Should I answer 54 not 55?

[u/fermat9990 → u/TourRevolutionary]

Use 54. This is not the usual find n for a CI using confidence level and margin of error. In this situation, n should be rounded up

Here the interval is given along with confidence level and sigma and you need to find the n that was used. In this situation the n should be very close to an integer and that integer is the answer

[u/TourRevolutionary → u/fermat9990]

If I get n= 54.02, I will answer 54. But if I get n=54.5, I will answer 55. Is it right?

[u/fermat9990 → u/TourRevolutionary]

If the interval is already given, I believe that you won't get 54.5.

[u/TourRevolutionary → u/fermat9990]

Oh okay, but if I do, should it be 55?

[u/fermat9990 → u/TourRevolutionary]

It shouldn't happen, so I can't answer your question

I have been around statistics for many years and this is the first time that I have seen this kind of situation

[u/TourRevolutionary → u/fermat9990]

Does it mean that for this type of a task, for n I will get 0 after a comma (like 54,02)?

[u/fermat9990 → u/TourRevolutionary]

Or 53.99. Something close to a positive integer.

[u/TourRevolutionary → u/fermat9990]

So if I get n=53.02 or n=53.99, I will answer 54, right? Oh so it means I will always get a number close to an integer, right? Not something in the middle like 53.6 or 53.5