Final answer:
Standard error in a hypothesis test measures the sampling variability, acting as the average deviation that occurs from repeated sampling, which affects test statistic reliability and confidence interval estimates.
Step-by-step explanation:
In a hypothesis test, standard error measures the sampling variability of a statistic. The standard error is essentially the standard deviation of the sampling distribution, which indicates how much a statistic varies from one sample to another, or in other words, it represents the average deviation that results from repeated sampling. When it comes to the mean, the standard error of the mean (SEM) is calculated as σ (population standard deviation) divided by the square root of n (sample size), although in practice we often use the sample standard deviation (s) as an estimate for σ when the population standard deviation is unknown.
Confidence intervals rely on the standard error to determine the range within which the true population parameter is likely to lie. For example, if we say that we are 90% confident that our confidence interval contains the true population mean, this implies that out of repeated samples, approximately 90% of those intervals will capture the actual population mean.