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Standardized test statistics are used in hypothesis testing. The general formula is: Standardized test statistic: (statistic-parameter)/(standard deviation of the statistic). The formula by itself doesn't mean much, unless you also know the three major forms of the equation for z-scores and t-scores.
Calculate the T-statistic Subtract the population mean from the sample mean: x-bar —. Divide s by the square root of n, the number of units in the sample: s ÷ (n).
Identify a sample statistic. Choose the statistic (e.g, sample mean, sample proportion) that you will use to estimate a population parameter. Select a confidence level. Find the margin of error. Specify the confidence interval.
To calculate the confidence interval, we must find p, q. p = 0.842 is the sample proportion. This is the point estimate of the population proportion. Since the requested confidence level is CL = 0.95, then = 1 CL = 1 0.95 = 0.05 (2) = 0.025.
In general, you compute the 95% confidence interval for the mean with the following formula: Lower limit = M — Z.95M. Upper limit = M + Z.95M. Where Z.95 is the number of standard deviations extending from the mean of a normal distribution required to contain 0.95 of the area and M is the standard error of the mean.

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