# Two-sample z test

The two-sample z-test is a statistical method used to compare the means of two independent samples to determine if they are significantly different from each other. It's a powerful tool in hypothesis testing, particularly when dealing with large sample sizes and when the population standard deviations are known. By calculating the z-score and comparing it to a critical value from the standard normal distribution, researchers can assess whether the observed difference between the sample means is due to chance or represents a true difference in the populations they represent.

Questions

- How do you find the p-value of a two tailed test when z = 1.95?
- How do you find a p value if n = 50 for a two-tailed test, and the test statistic z = 3.38?
- People with z-scores above 2.5 on an IQ test are sometimes classified as geniuses. If IQ scores have a mean of 100 and a standard deviation of 16 points, what IQ score do you need to be considered a genius?
- A researcher obtains #z = 2.04# for a one-sample #z# test. What is the decision for this test at a .05 level of significance?