Recent papers have reported that 54Mn, which decays by electron capture (a weak nuclear interaction) with half-life ~312 days, is influenced by solar activity. Should this actually occur, new physics would be needed to explain it. This paper reports results of an analysis of 54Mn activity measured over a time interval of ~3.6 half-lives. If standard nuclear physics applies, the logarithmic residuals of 54Mn activities should form a stationary set of independent random variables whose statistics are determined solely by a constant decay rate λ and initial mean count μ. Analysis of the time-variation, autocorrelation, and power spectra of the 54Mn logarithmic residuals agrees exquisitely with standard nuclear physics. Computer-simulated activities exhibiting periodic decay of amplitude show that anomalies would be detectable by these statistical tests for values of α as low as ~1 part in 104. This limit is about 10 times lower than reported deviations from exponential decay.