Simple "yes / no" question. Uncertain how to analyze the results I am in the midst of conducting a study which compares content in a printed catalog of records to content in a much larger online catalog of similar records. I have randomly selected 50 entries from the printed catalog and searched the online catalog to see if there are exact matches for these records. The results are 44 matches ("Yesses"), 6 non-matches ("Nos").  My hypothesis is that a significant number of records from the printed catalog will not be included in the online catalog. I have very, very little experience with statistical analysis and am unsure how to proceed. I appreciate any help or suggestions anybody can give me.
 A: If you chose your 50 entries at random from the printed catalog, then you can say that approximately 12% of your printed catalog entries don't appear online. (That is the 6 No are 12% of the 50 entries you looked for.)
The percentage has some amount of uncertainty since it's only a sample of the entries, so it's common to calculate a range of percentages, at some level of confidence. The Wikipedia article on the Binomial Proportion Confidence Interval has a good explanation in its first paragraph, given the choices of methods listed I'd skip down to the Bayesian alternative, the Jeffreys Interval. I believe this is calculated in R by:
> round (qbeta (c(0.025, 0.975), 0.5 + 6, 0.5 + 44), 2)
[1] 0.05 0.23

where the 0.025 and 0.975 represent the 95% significance interval, and you have 6 Missing and 44 Found. If I've done it correctly the answer is that there's a 95% confidence that the percentage of entries missing from the online catalog is in the range of 5% to 23%.
So the actual percentage of missing entries could be as low as 5% (and you got unlucky in your sample) or as high as 23% (more than 1 in 5), with a 95% chance that the actual percentage would fall within this range. (And therefore a 5% chance that the actual percentage would be less than 5% or more than 23%.) If you had looked for 200 random entries and 24 were missing, this would narrow the 95% interval to 8% to 17% -- four times the data to cut the interval in half.
This all depends on your experiment conforming to the requirements for using a Binomial distribution. For example, it assumes that the missingness of any two pages you chose are independent of each other. (That's why randomly choosing your entries is so important.)
There's no test to say if the number of missing entries is "significant". That's a matter of practical significance as determined by experts or decision makers.
