Test your knowledge of test-statistic values in statistical analysis

Hypothesis Testing for Population Mean

• The test-statistic value is a numerical value that helps determine whether to reject or fail to reject the null hypothesis about the population mean.
• The formula for calculating the test-statistic value for the population mean is: t = (x̄ - μ) / (s / √n), where x̄ is the sample mean, μ is the known population mean, s is the sample standard deviation, and n is the sample size.
• Factors that can affect the size of the test-statistic value include the sample size, sample standard deviation, and the difference between the sample mean and the known population mean.
• If the test-statistic value falls within the rejection region, it indicates that there is sufficient evidence to reject the null hypothesis, and it can be concluded that the population mean is likely to be different from the known value.
• The rejection region represents the area of the distribution where the null hypothesis can be rejected, and it is typically determined by the significance level (α) and the direction of the alternative hypothesis.
• If the test-statistic value falls outside the rejection region, it indicates that there is not sufficient evidence to reject the null hypothesis, and it can be concluded that the population mean is likely to be equal to the known value.