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I have 20-30 repeated measurements each of which produce a single number. My goal is to determine whether the mean of these numbers is statistically significantly greater than the number 1. (significantly less than 1 does not count, in this case)

I know, for example, that if I want to know whether the means of two populations are different, I can use a t-test, but this does not seem to apply when one of my "populations" is just the fixed number 1. Can anyone help suggest the correct test?

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    $\begingroup$ If you're prepared to assume independence (which may be doubtful with repeated measures) and common variance, and that the population is (sufficiently close to) normally distributed, see en.wikipedia.org/wiki/Student%27s_t-test#One-sample_t-test $\endgroup$ – Glen_b -Reinstate Monica Oct 23 '18 at 23:23
  • $\begingroup$ Erika was first, so I accepted their answer, but yes -- an upper tailed one-sample t-test is exactly what I'm looking for. @Glen_b I actually can assume independence in this case. $\endgroup$ – Bunji Oct 24 '18 at 3:06
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I would suggest using a One-Sample T-test. This site explains the procedure and also has a working example - http://www.biostathandbook.com/onesamplettest.html

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This is known as a one-sample t-test, as mentioned by Erika.

You can use the calculator here (and the information below the calculator for reference): https://stattrek.com/online-calculator/t-distribution.aspx

Make sure you select sample, in place of t-score.

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