# 3. Test Statistic and Significance Level

## c. explain a test statistic, Type I and Type II errors, a significance level, and how significance levels are used in hypothesis testing;

What is a test statistic? What is the typical formula for a test statistic?
- A test statistic is simply a number, calculated from a sample, whose value, relative to its probability distribution, provides a degree of statistical evidence against the null hypothesis.
- `test statistic = (sample statistic - parameter value under H_0) / standard error of sample statistic`

- “parameter value” is the number associated with the hypothesis. E.g. the “25%” in “25% of R&D costs are ultimately written off.”

What is the math notation for level of significance? - Also called the Alpha Level - \(\alpha\)

What is “level of significance”? The level of significance is the probability of rejecting the null hypothesis (invalidating it) when it is actually true. Also called the Alpha level. Also called a Type I error. It is commonly set to 5%, but can be 1% or 10%.

Are Alpha Level and Significance Level the same thing? Yes

If a test result is said to statistically significant at the 5% level, is your null hypothesis rejected or not rejected? It is rejected. The actual wording is “The result would be unexpected if the null hypothesis were true”

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CFA

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- 115.020.60 Reading 11 - Hypothesis Testing to 115.020.60.03 Reading 11 - 3. Test Statistic and Significance Level