Introduction to Hypothesis Testing for One Population Mean

Recall that we reject the null hypothesis and conclude that we have statistical significance if our p-value is less than the significance level \(\alpha\). Now we extend these ideas into hypothesis testing about means, first focusing on a single population mean.

Note the following three notes of caution:

• Your sample must be representative of the population.
  • One way to get representative sample is a random sample
• Hypotheses/conclusions apply to larger populations represented by the samples.
• If the distribution is highly skewed, consider analyzing by the median rather than the mean – nonparametric methods.

Basic Steps

1. Determine \(H_0\) and \(H_A\)
2. Verify necessary data conditions.
3. For proportions, the standardized statistic is called a z statistic which has the \(N(0,1)\) distribution.
4. For means, the standardized statistic is called a t statistic which has a t distribution.
5. Find the p-value.
6. Decide if the result is statistically significant based on the p-value.
7. Report conclusion in the context of the situation.