Only if the rest of the assumptions of samples are met. 176 is large enough for significance, providing the sample is properly drawn. If the folks asking for the cigarettes weren't asking exactly the same way each time (expectations influencing decisions) then the sample size is irrelevant. If all the people in the nightclub were within a couple years of each other, it's not valid to expand to everyone in the population. If it is not a valid sample the simple statistical methods cannot be used. If the sample is bad enough, statistics are just not valid.
The classic example of problems with samples is a telephone survey for a presidential race--back when only the wealthy had telephones. The survey results were very strong via the p-value check--and completely wrong because the sample population and the actual population were completely different. It was an accurate measure of what people with telephones thought. It was not an accurate measure of what the voters as a whole thought, as it wasn't a sample drawn from all voters.
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Only if the rest of the assumptions of samples are met. 176 is large enough for significance, providing the sample is properly drawn. If the folks asking for the cigarettes weren't asking exactly the same way each time (expectations influencing decisions) then the sample size is irrelevant. If all the people in the nightclub were within a couple years of each other, it's not valid to expand to everyone in the population. If it is not a valid sample the simple statistical methods cannot be used. If the sample is bad enough, statistics are just not valid.
The classic example of problems with samples is a telephone survey for a presidential race--back when only the wealthy had telephones. The survey results were very strong via the p-value check--and completely wrong because the sample population and the actual population were completely different. It was an accurate measure of what people with telephones thought. It was not an accurate measure of what the voters as a whole thought, as it wasn't a sample drawn from all voters.