# Statistical test evaluating consistency

I'm trying to solve a problem and I'm not used to how little data I'm given. I'm trying to compare results from an actual system I've created, and a value given to me. I've found that the value of Model A's mean is 10.871, for instance, and I have also found the standard deviation, sample size, and half width of Model A. I'm supposed to compare Model A's mean to another mean from the "real" mean, which is appx 14. I'm not given the standard deviation, sample size, or any information about the "real" mean, other than it being 14. I need to use the level of significance alpha = 0.05, but none of the t-tests or z-tests seem to work since I don't know standard deviation or sample size for the "real" mean. How can I carry out my test to see whether or not the "real" mean is consistent with the mean I've found from Model A?

You are comparing one sample (mean = 10.871, sd known) with a specified mean (14). If you really want to do a null hypothesis significance test (many experienced statisticians deprecate them) and can assume [approximate] Normality, then a one-sample Student's t-test is appropriate, you can Google that for more detail but briefly:

The test statistic is $$t = \frac{m-μ}{s/\sqrt n }$$
where
m = sample mean
μ = hypothesized population mean
s = sample standard deviation
n = sample size

The p-value depends on the alternative hypothesis
$$H_1: m > μ$$ then $$P(t_{n-1} >= t)$$
$$H_1: m < μ$$ then $$P(t_{n-1} <= t)$$
$$H_1: m != μ$$ then $$2 * P(t_{n-1} >= |t|)$$

This is an unreplicated design question. You cannot use any of those tests and the best you can do is say that the "real mean" falls within x% confidence interval of your model. It is easy to illustrate why such test would be useless: you could model a population with a mean of 14 and a range of e.g. 0-28 and one with the same mean and a range of 13.999-14.001, or much more extreme and skewed cases, so without knowing the underlying distribution of the 'real' population, it is impossible to predict whether and to what degree the two distributions overlap.