Hypothesis testing

Japanese school year: Math B

What you learn

You will learn how to set null and alternative hypotheses, calculate test statistics, and determine rejection using significance levels. This method is widely used in comparing product performance and determining scientific significance. Familiarity with the normal distribution and interval estimation will help you master this topic.

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Key points

Use this formula to calculate the test statistic $Z$ , which standardizes how far the sample mean $\bar{X}$ is from the baseline mean $m_0$ . Here, $\sigma$ is the population standard deviation and $n$ is the sample size.

Z = \frac{\bar{X} - m_0}{\frac{\sigma}{\sqrt{n}}}

Use this formula to calculate the test statistic $Z$ , testing how far the sample proportion $R$ deviates from the baseline proportion $p_0$ . Here, $n$ is the number of surveyed samples.

Z = \frac{R - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}

Use this rejection rule to judge if the difference $|Z|$ is too large to be just chance at the 5% level. If $|Z|$ is 1.96 or greater, we conclude the original assumption was incorrect.

|Z| \ge 1.96

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Practice 1Coming soon