# Hypothesis Tests of Mean with Changing Sample Mean

Move the slider for μ to change the population mean. Move the slider for s to change the sample standard deviation. Move the slider for size to change the sample size. Move the slider for α to change the level of significance/confidence. Move the type slider to select the test type: left-tailed, right-tailed, two-tailed. Move the P-value/Critical Value slider to change from the P-value approach to the critical value approach, or visa versa. Move the slider for xbar to see how the conclusion changes as the sample mean changes.
The P-value is the probability of obtaining a test statistic as extreme as the one for the current sample under the assumption that the null hypothesis is true. For a one-tailed test, the critical value is the standard score such that the area in the tail on the opposite side of the critical value from zero equals the corresponding significance level, α . For a two-tailed test, there is a negative critical value and a positive critical value. The negative critical value is such that the area in the tail below it is equal to α divided by two. The positive critical value is the opposite of the negative critical value.