It's not big enough to say anything about the larger population even at that college, no. It actually reminds me of Neil Malamuth's research from the 1980s that I've posted about before, where 16 to 20 percent of respondents would commit "rape" if they could be certain of getting away with it, but 36 to 44 percent if it was worded as "force a woman to have sex."
How do you get "31.7%" of 73 men, by the way? That's 23.141 men.
That is disturbing. However, is 73 enough people for a sample?
73 men doesn't feel like big enough of a sample. Still, these results are very disturbing.
Regarding bolded, yes, and no, It depends more on how precise you want your confidence interval to be than the actual population size which is largely irrelevant unless you've a small population/are sampling a high percentage of the population.
At 73 people, for a large population, at the 95% confidence interval, your margin of error is going to be approximately 11.47%. The population size, if large, is rather irrelevant. As a simple demonstration of how irrelevant it is, the margin of error for 1,000,000,000,000 people is approximately 11.47%. At 1,000,000,000 people is approximately the same, at 100,000 people it's approximately the same, at 1,000 people it's approximately 11.05%. A rough way of checking the margin of error for a large population, so long as the sample is a small percentage of the overall population (I know I'm being vague but I don't care to explain at the moment) is .98 divided by the square root of the (sample size) (i.e. 98/((100)((sample size)^(1/2)) or .98 multiplied by (sample size)^(-(1/2))).
Original Claim: 36% of men would 'force a woman to have sex' if they'd get away with it.
Let's say there was another study, where 1,000 people were sampled from the population. In it, 431 respondents say they would 'force a woman to have sex' if they'd get away with it.
H0 - We do not prove the original study wrong.
H1 - We prove the original study wrong.
4310/10000 is approximately 43%.
Original study found 36% would with a sample size of 73.
At the 95% Confidence interval:
.98/(73)^1/2 is approx 11.47%.
Therefore the range that the true percentage is, if the study is accurate (36-11.47)% <= p <= (36+11.47)% (I'm not doing these calculations. 43% falls within these ranges, so we fail to reject the null hypothesis (i.e. we would not be able to claim the original study was flawed) despite the fact that it's a much larger population.
That's an example simplified hugely and making a number of assumptions, but with that amount of people you can be 95% certain that the true percentage will be within the range.
(Basically, if the sampling was done correctly, the population is pretty much irrelevant if it's very large; I should also note that I've only done Statistics at a Leaving Certificate level so perhaps there are more intricacies than we had been led to believe, as I assume, but I very much doubt it's hugely inaccurate).
Regarding underlined,that's odd.
EDIT: Also, supports Neil Malamuth's research assuming he found 40% would do it and it was +-4% at 95% confidence interval (because this research states 24.53% to 47.47% would)
EDIT 2: Terrisus could probably give more accurate calculations than the extemely broad stuff I've done though, and talk about other confidence intervals (the Leaving Certificate was confined to 95% and rough estimations) though, but it's better to criticise the selecting of a sample than it is for it being too small.
It's such a dumb fun movie! You really should watch it. I'm almost tempted to suggest a viewing party, haha.
