P-Value Analyzer

A: The Sample Mean (x̄) is the average of the sample data you have collected. You can calculate it by adding up all the data points and then dividing by the number of data points. For example, if your sample data is 4, 5, 6, 7, and 8, the sample mean would be $\frac{4+5+6+7+8}{5}=6$.

A: The Population Mean (μ) represents the true average of the entire population. It’s often an established or expected value. In some cases, you might have this value from previous studies or it might be a benchmark value. If you’re testing whether a new method is better than an old one, the performance of the old method could serve as your population mean.

A: The standard deviation (σ) measures the amount of variation or dispersion from the mean. If you’re using statistical software, it often provides this value when you’re looking at the descriptive statistics of your data. If calculating by hand, you’d find the average of the squared differences from the Mean and then take the square root of that result.

A: The sample size (n) tells us how many data points or observations are in your sample. It’s crucial for determining the standard error and for understanding the reliability of your sample mean. Larger sample sizes generally provide more reliable results.

A: The significance level (α) is the probability of rejecting the null hypothesis when it’s actually true. Common choices are:

• 0.05 (95% Confidence): This is the most common and means there’s a 5% chance of making a Type I error.
• 0.01 (99% Confidence): More stringent, with only a 1% chance of making a Type I error.
• 0.10 (90% Confidence): Less stringent, with a 10% chance of making a Type I error.

The right significance level often depends on your field of study and the specific test you’re conducting.