ztestillä

ztestillä is a term that refers to the use of a z-test in statistical analysis. A z-test is a hypothesis test used to determine whether a sample mean is statistically different from a known population mean, or to compare the means of two samples when the population variances are known and the sample sizes are large. The z-test is based on the z-statistic, which measures how many standard deviations a sample mean is from the population mean.

The z-test is appropriate when the population standard deviation is known and the data is normally distributed, or when the sample size is large enough (typically n > 30) for the Central Limit Theorem to apply, ensuring the sampling distribution of the mean is approximately normal. There are two main types of z-tests: a one-sample z-test, which compares a single sample mean to a known population mean, and a two-sample z-test, which compares the means of two independent samples.

The process of conducting a z-test involves formulating a null hypothesis (H0) and an alternative hypothesis (H1). The null hypothesis typically states there is no significant difference, while the alternative hypothesis suggests there is a difference. A z-statistic is calculated from the sample data, and this value is then compared to a critical value from the standard normal distribution or used to determine a p-value. If the calculated z-statistic falls into the rejection region (determined by the chosen significance level, alpha), or if the p-value is less than alpha, the null hypothesis is rejected in favor of the alternative hypothesis. This indicates a statistically significant difference between the sample and population means, or between the two sample means.