DC-Den

What is a Z score or Z statistics? Firstly Z score and Z statistics is the same. It is a measure of the number of standard deviations a data point is away from the sample mean. Mathematically this is written as: `z = (x - bar x) / sigma` where `z` = Z score or Z statistics `x` = data point `bar x` = sample mean `sigma` = sample standard deviation The mathematical equation of standard deviation is: `sigma = sqrt((x - bar x)/N)` where `N` = number of sample points What is P value? The P value is the probability that a particular value assuming the null hypothesis is true. Conventionally a P value of less than 0.05 is grounds for rejecting the null hypothesis. For the lower-tailed test or left-tailed test, the P value is expressed as: `P = Pr(TS <=ts | H_0) = cdf(ts)` And for the upper-tailed test or right-tailed test, the P value is expressed as: `P=Pr(TS>=ts |H_0) = 1-cdf(ts)` And the P value for a two-tailed test is `P = 2 xx min{Pr(TS<=ts |H_0), Pr(TS>...

Recently I assessed the power consumption of a particular server rack to determine if we had sufficient power capacity remaining to support additional server installation. Note: For my intent and purposes, the names and values have been obscured and changed to maintain confidentiality. The power capacity of the rack was 2.5 kW, while the average measure power consumption was 2.16 kW. This suggested that the remaining capacity = 2.5 - 2.16 = 0.34 kW But making decision based on a single aggregated point seems risky. So I calculated the confidence interval range instead. What is Confidence Interval The confidence interval is the value range where the mean of the population can be found based on the sample data collected. Mathematically, `CI = bar x pm z s/sqrt(n)` where `CI = "confidence interval"` `bar x = "sample mean"` `z = "confidence level value, e.g. 95%"` `s = "sample standard deviation"` `n = "sample siz...