Relative size of a p-value for a second hypothesis, compared to the first.

#1
Hi all,

I apologise in advance if this is a very easy question - I may be struggling with the wording, or I might just be a bit slow.

The obtained p value for a correlation analysis is .036 where n = 50. If an analysis had been undertaken with n = 90, and the same sample correlation value was obtained, what would be the relative size of the p value for the second hypothesis test compared to the first? And why?

I'm thinking the question's asking me to say the size of the p value for the second hypothesis test compared to the original would be smaller because as the sample size increases, the standard error decreases. The p value is a function of the standard error, where the smaller the standard error, the smaller the p value. The p value would be larger for n=50 due to the increase in standard error.

Is this correct, or have I got it around the wrong way?

Thanks so much in advance!
 
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